Methods of improving the measurement of knee stress in ion-exchanged chemically strengthened glasses containing lithium

ABSTRACT

Methods of improving the measurement of knee stress in an ion-exchanged chemically strengthened Li-containing glass sample that includes a knee are disclosed. One of the methods includes compensating for a shift in the location of the TIR-PR transition location associated with the critical angle location, wherein the shift is due to the presence of a leaky mode. Another method includes applying select criteria to the captured mode spectra image to ensure a high-quality image is used for the knee stress calculation. Another method combines direct and indirect measurements of the knee stress using the mode spectra from multiple samples to obtain greater accuracy and precision as compared to using either the direct measurement method or the indirect measurement method alone. Quality control methods of forming the glass samples using measured mode spectra and related techniques for ensuring an accurate measurement of the knee stress are also disclosed.

CROSS-REFERENCE TO RELATED APPLICATIONS

This application claims the benefit of priority under 35 U.S.C. § 119 ofU.S. Provisional Application Ser. No. 62/538,335 filed on Jul. 28, 2017,the content of which is relied upon and incorporated herein by referencein its entirety.

FIELD

The present disclosure relates to chemically strengthened glass, and inparticular relates to methods of improving the measurement of kneestress in ion-exchanged chemically strengthened glasses containinglithium.

BACKGROUND

Chemically strengthened glasses are glasses that have undergone achemical modification to improve at least one strength-relatedcharacteristic, such as hardness, resistance to fracture, etc.Chemically strengthened glasses have found particular use as coverglasses for display-based electronic devices, especially hand-helddevices such as smart phones and tablets.

In one method, the chemical strengthening is achieved by an ion-exchangeprocess whereby ions in the glass matrix are replaced by externallyintroduced ions, e.g., from a molten bath. The strengthening generallyoccurs when the replacement ions (i.e., in-diffusing ions) are largerthan the native ions (e.g., Na+ ions replaced by K+ ions). Theion-exchange process gives rise to a refractive index profile thatextends from the glass surface into the glass matrix. The refractiveindex profile induced by potassium has a depth-of-layer or DOL thatdefines a size, thickness or “deepness” of the ion-diffusion layer asmeasured relative to the glass surface. Said index profile alsocorrelates with a number of stress-related characteristics, includingstress profile, surface stress, center tension, knee stress,birefringence, etc. The refractive index profile may define an opticalwaveguide when the profile meets certain criteria.

Recently, chemically strengthened glasses with a very large depth ofcompression (DOC) have been shown to have superior resistance tofracture upon face drop on a hard rough surface. Glasses that containlithium (“Li-containing glasses”) can allow for fast ion exchange (e.g.,Li+ exchange with Na+ or K+) to obtain a large DOC. Note that in suchglasses DOC does not necessarily correspond to the potassium-definedDOL, and is in many cases much larger than that DOL.

An example stress profile of particular commercial importance includesfirst region near the substrate surface characterized by rapid or“spike” change in refractive index and stress and a second region deeperin the substrate where the refractive index can vary slowly and can besubstantially the same as the bulk refractive index. The location wherethe first and second regions of the profile meet is called the kneebecause the stress profile curve at the transition between the tworegions has a knee-shaped sudden change in slope. The spike portion ofthe profile is particularly helpful in preventing fracture when glass issubjected to force on its edge (e.g., a dropped smart phone) or when theglass experiences significant bending. The spike can be achieved inLi-containing glasses by ion exchange in a bath containing KNO₃.

It is often preferred that the spike be obtained in a bath having amixture of KNO₃ and NaNO₃ so that Na+ ions are also exchanged. The Na+ions diffuse faster than K+ ions and thus diffuse at least an order ofmagnitude deeper than the K+ ions. Consequently, the deeper sectionregion of the profile is formed mainly by Na+ ions and the shallowportion of the profile is formed mainly by K+ ions.

Because the Na for Li exchange does not produce a substantial increasein the refractive index, the deeper second region of the profile usuallydoes not support guided modes, i.e., does not define a waveguide.Furthermore, in lithium containing glasses similar to the Li-containingCorning Gorilla® 5 glass, compressive stress induces a relativerefractive index decrease for the component parallel to the stress,which leads to decrease of the relative refractive index of thetransverse electric (TE) optical wave in a chemically strengthened glasssheet.

For chemically strengthened Li-containing glasses to be commerciallyviable as cover glasses and for other applications, their quality duringmanufacturing must be controlled to certain specifications. This qualitycontrol (QC) depends in large part on the ability to control theion-exchange process during manufacturing, which requires the ability toquickly and non-destructively measure important parameters of therefractive index and stress profiles, and in particular the knee stressCSk, which occurs at the knee of the profile where distribution of Kions exchanged into the substrate abruptly tapers off to a region in thesubstrate where the local compressive stress is generated substantiallyby Na ions diffused into the glass.

Presently, direct measurements of the knee stress CSk are particularlydifficult in cases where the second region does not support guidedwaves. Direct measurements can also be adversely affected by measurementconditions such as sample warpage, illumination non-uniformities, andreduced image quality of the captured mode spectra. In addition, thepresence of guided or leaky modes very close to the critical angle canreduce the measurement conditions (measurement window) for adequatelydetermining the critical angle, which is the location wheretotal-internal reflection (TIR) transitions to partial reflection (PR).This location is needed to accurately determine the knee stress CSk bythe direct method. The inability to adequately characterize the kneestress CSk over a relatively wide measurement window has hindered themanufacturing of chemically strengthened Li-containing glasses becausethe knee stress is a key parameter used in quality control when formingchemically strengthened Li-based glass products with superiordrop-fracture resistance, such as Gorilla® glass made by Corning, Inc.,of Corning, N.Y.

SUMMARY

Methods of performing non-destructive, direct measurements of the kneestress CSk are disclosed in U.S. Patent Application Publication No.2016/0356760, while methods of performing non-destructive indirectmeasurements of the knee stress CSk are disclosed in U.S. PatentApplication Publication No. 2017/0082577 (issued as U.S. Pat. No.9,897,574), all of which are incorporated by reference herein.

As noted above, a major limitation of the previously disclosed directmethod of measuring CSk is a limited measurement window or “sweet spot.”In the preferred measurement window, both the TM and TE effectiveindices at the depth of the knee are relatively far away from effectiveindices associated with TM and TE guided and leaky modes, which allowsone to obtain an accurate determination of the critical angle location,as described below.

Another limitation that occurs particularly in some cases ofprism-coupling angular spectra after first-step chemical strengthening,is the relatively poor precision of detecting the critical angle for theTE mode, even when the spectrum is in the “sweet spot.” One of theindirect methods based the spike-stress-slope can avoid these issues,but its precision becomes inadequate when the spike slope is very high(such as >60 MPa/micron), which is characteristic of most currentlypracticed second-step profiles near the surface. Furthermore, thismethod is only accurate when the TM (the upper) transition is strictlyin the “sweet spot,” otherwise a significant systematic error can beinduced.

In addition, the double-ion-exchange (DIOX) process complicates theextraction of CSk by using the stress-slope-method because the sweetspot is small and because the DIOX process introduces significantuncertainty in the extrapolation of the estimated slope beyond thehighest-order mode to the critical-angle index.

The indirect method based on utilizing the relationship between CSk andthe birefringence of the highest-order guided mode suffers fromsignificant systematic errors when the conditions of chemicalstrengthening deviate substantially from a reference condition. It hasbeen found that this is problematic for manufacturing operations thatare focused on minimizing cost and that utilize unskilled labor. In mostcases, the restrictions on the fabrication process and productattributes imposed by the requirement for validity of CSk measurementsby this method are much tighter than the restrictions dictated by themechanical-performance requirements. Usually these tight restrictionsfor QC metrology validity are viewed by the strengthening operations asunnecessary and costly.

The ideal method for measuring CSk for QC is non-destructive, fast,precise, and accurate, and has at best only small systematic errors overa range of measurement conditions (i.e., over a large measurementwindow) so that an out-of-specification product (sample) does not passfor an in-specification product (sample) by a combination of systematicerrors that makes it appear in-specification.

The present disclosure is thus directed to methods of improving theprecision and accuracy of the direct method of measuring CSk ofchemically strengthened glass samples formed by ion-exchange andcontaining lithium. In particular, the methods widen the “sweet spot”for such glass samples where the accuracy of the method is consideredgood. Furthermore, methods of QC are disclosed that take advantage ofthe improved direct method of CSk measurement and use the improveddirect methods in combination with an indirect method to improve theoverall CSk measurement.

In one aspect of the disclosure, methods of direct CSk measurement aredisclosed, where one or more sources of systematic, random, andquasi-random error are mitigated, allowing for more precise directmeasurements of CSk within the previously defined “sweet spot,” and inaddition, widening of the range of angular coupling spectra over whichdirect-CSk measurements with acceptable accuracy and precision areenabled. This effectively widens the measurement window to almost thefull range of possible angular-coupling spectra, with only very narrowregions of spectral space in which direct CSk measurements are lessreliable and subject to larger errors.

The methods disclosed herein are generally directed to makingmeasurements of the knee stress CSk for chemically strengthenedLi-containing glasses having a stress profile that has a knee. Such aprofile is produced by an ion-exchange process whereby Li+ (the nativeion) is exchanged with (in-diffusing) K+ and Na+ ions (i.e., Li+⇔K+,Na+). An example of a stress profile having a knee includes a firstregion adjacent the substrate surface and that is spiked (and thus isalso referred to the spike region or just “spike”) and a second regionthat is more gradual (e.g., has a much smaller slope of stress withdepth, and may be approximated as following a power law) in a largerportion of the interior (“deep region”) of the substrate. The knee isdefined by the relatively abrupt transition between the first and secondregions. The spike is generally formed by the slower diffusion (and thusshallower) K+ ions while the deeper region is formed by the faster (andthus deeper) diffusing Na+ ions.

Another aspect of the methods disclosed herein is directed to performingQC of the glass samples being processed. Such quality control isimportant for a commercially viable manufacturing process. The QCmethods include adjusting the DIOX process parameters for fabricatingIOX articles based on measurements of the knee stress CSk of fabricatedIOX articles.

Another aspect of the disclosure is a method of improving a measurementof knee stress CSk in a chemically strengthened Li-containing glasssample having a warped surface and a body and that includes a stressprofile having a knee. The method comprises: capturing an image of atleast one of a TE mode spectrum and a TM mode spectrum; measuring aslope of light intensity at a transition between the total-internalreflection and the partial-internal reflection sections of the modespectrum (i.e., the TIR-PR transition) and measuring a width of theTIR-PR transition for at least one of the TE mode spectrum and TM modespectrum; and comparing the measured slope and the measured width to aslope threshold and a width threshold WT_(TIR-PR) associated withreference glass sample having a flat surface.

Another aspect of the disclosure is a method of improving a measurementof knee stress CSk in a chemically strengthened Li-containing glasssample having a surface and a body and that includes a stress profilehaving a knee and that defines a waveguide that supports light as guidedwaves and a leaky mode. The method comprises: capturing an image of a TEmode spectrum and a TM mode spectrum of the guide waves and leaky mode;measuring a position of maximum slope of a transition between atotal-internal reflection and a partial-internal reflection (TIR-PR) forthe light supported in the waveguide for each of the TE mode spectrumand the TM mode spectrum; determining from the TE and TM mode spectra aposition of the leaky mode as a relative minima after the TIR-PRtransition; determining from the leaky mode position an amount of shiftin the TIR-PR position caused by the leaky mode; adding the amount ofshift from the measured position of the TIR-PR transition to arrive at acorrected TIR-PR transition location; and using the corrected TIR-PRtransition location to determine the knee stress.

Another aspect of the disclosure is a method of improving a measurementof a knee stress in a chemically strengthened Li-containing glass samplehaving a surface and a body and that includes a stress profile having aknee and that defines a waveguide that supports light as guided modes.The method comprises: capturing an image of a TE mode spectrum and a TMmode spectrum; measuring a slope of a transition between atotal-internal reflection and a partial-internal reflection (TIR-PR) forthe light supported by the waveguide for each of the TE mode spectrumand the TM mode spectrum; and comparing the slope to a steepnessthreshold STH and using the slope to determine a location of the TIR-PRtransition and using the corrected TIR-PR transition location todetermine the knee stress only if the slope is greater than the selectsteepness threshold.

Another aspect of the disclosure is a method of measuring a knee stressin chemically strengthened Li-containing glass samples each having asurface and a body and that includes a stress profile having a knee andthat defines a waveguide that supports light as guided modes in thespike region which has a monotonically decreasing index profile. Themethod includes: measuring TE and TM mode spectra for each of themultiple glass samples; for each of the measured TE and TM mode spectra,directly measuring a knee stress CSk^(direct) and also indirectlymeasuring the knee stress via CSk^(direct)=β_(x)F₄, where β_(x) is alast-mode birefringence and F₄ is a scaling factor; calculating a movingaverage F₄ ^(average) for the scaling factor F₄ using the directlymeasured knee stresses CSk^(direct) via the relationshipF₄=CSk^(direct)/β_(x); and calculating a hybrid knee stressCSk^(hybrid)=β_(x)F₄ ^(average).

Another aspect of the disclosure is a method of ensuring an accuratemeasurement of knee stress in a chemically strengthened Li-containingglass sample having a surface and a body and that includes a stressprofile having a knee and that defines a waveguide that supports lightas guided modes. The method includes: capturing TE mode spectrum and aTM mode spectrum respectively comprising TE fringes and TM fringes;measuring a slope SLP of a transition between a total-internalreflection and a partial-internal reflection (TIR-PR) for the lightsupported by the waveguide for each of the TE mode spectrum and the TMmode spectrum; and comparing the slope to a steepness threshold STH andusing the slope to determine a a location of the TIR-PR transition andusing the corrected TIR-PR transition location to determine the kneestress only if the slope is greater than the select steepness thresholdSTH.

Another aspect of the disclosure is a method of ensuring an accuratemeasurement of knee stress in a chemically strengthened Li-containingglass sample having a surface and a body and that includes a stressprofile having a knee and that defines a waveguide that supports lightas guided modes. The method includes: irradiating the glass sample bydirecting light from a light source as a light beam through a couplingprism and to the surface of the sample to generate an angularillumination spectrum; detecting the angular illumination spectrum at adigital sensor to capture TE mode spectrum and a TM mode spectrumrespectively comprising TE fringes and TM fringes and respectivetotal-internal reflection and a partial-internal reflection (TIR-PR)transitions associated with a critical angle and that define respectivecritical angle effective index values n_(crit) ^(TE) and n_(crit) ^(TM);measuring an intensity gradient in the angular illumination spectrum inthe vicinity of the TIR-PR transitions; and proceeding with themeasurement of the knee stress only if the measured intensity gradientis less than an intensity gradient threshold.

Another aspect of the disclosure is method of performing quality controlof an IOX process used to form chemically strengthened Li-containingglass samples having a surface and a body and that includes a stressprofile having a spike and a knee and that defines a waveguide thatsupports light as guided modes. The method includes: for each of aplurality of glass samples formed by the IOX process, measuring TE andTM mode spectra of the guided modes for each of the glass samples;comparing the measured TE and TM mode spectra to reference TE and TMmode spectra of at least one reference glass sample formed using thesame IOX process and having a flat surface; and adjusting the IOXprocess to maintain the measured TE and TM mode spectra to be within atleast one mode spectrum tolerance of the reference TE and TM modespectra. The adjustment can include one or more of changing thediffusion temperature, the diffusion time and the ion concentration ofeither or both of the in-diffusing ions, which in an example are K+ andN+.

Additional features and advantages are set forth in the DetailedDescription that follows, and in part will be apparent to those skilledin the art from the description or recognized by practicing theembodiments as described in the written description and claims hereof,as well as the appended drawings. It is to be understood that both theforegoing general description and the following Detailed Description aremerely exemplary, and are intended to provide an overview or frameworkto understand the nature and character of the claims.

BRIEF DESCRIPTION OF THE DRAWINGS

The accompanying drawings are included to provide a furtherunderstanding, and are incorporated in and constitute a part of thisspecification. The drawings illustrate one or more embodiment(s), andtogether with the Detailed Description serve to explain principles andoperation of the various embodiments. As such, the disclosure willbecome more fully understood from the following Detailed Description,taken in conjunction with the accompanying Figures, in which:

FIG. 1A is an elevated view of an example Li-containing glass substratein the form of a planar substrate, into which ion exchange of both Kions and Na ions is performed;

FIG. 1B is a close-up cross-sectional view of the ion exchangedsubstrate of FIG. 1A as taken in the x-z plane and that illustrates theK and Na ion-exchange process that takes place across the substratesurface and into the body of the substrate;

FIG. 1C schematically illustrates the result of the ion exchange processthat forms the ion-exchanged substrate;

FIG. 2A is a representation of an example refractive index profilen^(TM)(z) for the ion exchange substrate illustrated in FIG. 1C for theTM polarization;

FIG. 2B is the same plot as FIG. 2A, but for the n^(TE)(z), i.e., forthe TE polarization;

FIG. 2C is a plot of the stress σ(z) versus the depth coordinate z forthe corresponding refractive index profiles of FIGS. 2A and 2B and showsthe spike (SP), the knee (KN) and the depth of compression (DOC);

FIG. 3A is a schematic diagram of an example prism-coupling systemaccording to the disclosure and that is used to measure IOX articlesusing the methods disclosed herein;

FIG. 3B is a close-up view of the photodetector system of theprism-coupling system of FIG. 3A;

FIG. 3C is a schematic representation of an example measured modespectrum;

FIG. 3D is a schematic representation of an example measured modespectrum of a Li-containing glass formed by an ion-exchange processusing a mixture of NaNO₃ and KNO₃, with the mode spectrum including TM(top) and TE spectra (bottom), and also showing profile measurementparameters as explained below;

FIGS. 3E through 3G are schematic diagrams of a portion of an example TMmode spectrum illustrating how the location of the transition betweentotal-internal reflection and partial-internal reflection (i.e., theTIR-PR location) can shift due to the presence of a leaky mode close tothe TIR-PR location;

FIG. 4 is a plot of the stress (MPa) versus a normalized positioncoordinate z/T, showing the model stress profile (solid line) for asample chemically strengthened Li-containing glass that has undergone aK+ and Na+ ion exchange, wherein the dashed line represents the modelprofile for Na+ diffusion only, noting that the model profile has ionexchange taking place at two surfaces that respectively reside atz/T=−0.5 and +0.5;

FIG. 5A is a schematic representation of a measured mode spectrumshowing the TE and TM mode spectra for an example chemicallystrengthened Li-containing glass sample;

FIG. 5B is a schematic diagram of the TIR-PR transition illustrating howthe slope of the TIR-PR transition in the measured mode spectrum changesdue to a warped IOX article;

FIG. 5C is a schematic diagram of an example leaky mode resonanceillustrating example measurement parameters used in correcting for ashift in the TIR-PR transition location;

FIG. 6 depicts a flow diagram of an example hybrid method of measuringCSk that combines both direct and indirect measurement methods fordetermining CSk.

DETAILED DESCRIPTION

Reference is now made in detail to various embodiments of thedisclosure, examples of which are illustrated in the accompanyingdrawings. Whenever possible, the same or like reference numbers andsymbols are used throughout the drawings to refer to the same or likeparts. The drawings are not necessarily to scale, and one skilled in theart will recognize where the drawings have been simplified to illustratethe key aspects of the disclosure.

The claims as set forth below are incorporated into and constitute partof this Detailed Description.

The term “IOX article” and “glass sample” are used interchangeablyherein.

In the discussion below, the transition between total-internalreflection and partial-internal reflection in a given mode spectrum isreferred to as the TIR-PR transition, and the location of the TIR-PRtransition is referred to as the TIR-PR location.

The terms “ion exchange” and “ion exchanged” are both represented by theacronym IOX, and it will be apparent from the context of the discussionwhich term applies. The acronym DIOX means either “double ion exchange”or “double ion exchanged.”

The acronyms TE and TM respectively stand for “transverse electric” and“tranverse magnetic” and refer to the direction of the electric andmagnetic fields of the guided waves supported by the IOX region formedin the glass substrate as described below. The TE and TM guided wavesare also referred to below as “TM waves” and “TE waves.”

The term “resonance” is another word for a fringe in a mode spectrum,since the intensity distribution of a fringe has the shape of aresonance curve as known in the art and can have either an intensitypeak or an intensity dip, depending on the measurement configuration ofthe prism coupling system that captures the TM or TE mode spectra (see,e.g., FIG. 3E and the mode fringe 252TM).

The terms “slope threshold” and “steepness threshold” are synonymous asused herein.

Example IOX Process in Li-based Glass

FIG. 1A is an elevated view an example IOX article 10 formed from aglass substrate 20 using an IOX process. The example glass substrate 20is planar and has a body 21 and a (top) surface 22, wherein the body hasa base (bulk) refractive index n_(s), a surface refractive index n₀ anda thickness T in the z-direction. FIG. 1B is a close-up cross-sectionalview of the glass substrate 20 as taken in the y-z plane and illustratesan example IOX process that takes place across surface 22 and into body21 in the z-direction to define an IOX substrate 20 that constitutes theIOX article 10. The body 21 is constituted by the glass matrix of theIOX substrate.

In an example, the IOX articles 10 are formed using a DIOX process in aLi-containing glass. In one example, the DIOX process utilizes twodifferent types of ions, namely Na+ and K+, to replace another differention Li+ that is part of the glass body 21. The Na+ and K+ ions can beintroduced into the glass body 21 either sequentially or concurrentlyusing known IOX techniques, and may be introduced concurrently in one ormore IOX steps. As noted above, the Na+ ions diffuse faster than the K+ions and thus go deeper into the glass body 21. In other words, anexample DIOX process in the present disclosure means that both K+ andNa+ were introduced in the glass during ion exchange, and does notnecessarily mean that two IOX steps were performed.

FIG. 1C is a schematic diagram of the resulting DIOX process, and FIGS.2A and 2B are representative example refractive index profiles n^(TM)(z)and n^(TE)(z) for the TM and TE polarizations, respectively, for the IOXsubstrate 20 having undergone the DIOX process such as shown in FIG. 1C.The associated stress profile can be represented by σ(z) and is shown inFIG. 2C.

The IOX process defines an IOX region 24 in the glass body 21. Therefractive index profile n(z) and the IOX region 24 each includes afirst “spike” region R1 associated with the shallower ion-exchange (K+ions) and that has a depth D1 into body 21 that defines a“depth-of-layer for the spike” denoted hereinafter as DOL_(sp), orsimply DOL. In the present disclosure the acronym DOL is usedexclusively to mean DOL_(sp) unless specified explicitly otherwise. Therefractive index profile n(z) also includes a second region R2associated with the deeper ion-exchange (Na+ ions) and that has a depthD2 that may extend all the way to the middle of the substrate. A knee KNis located at the bottom of the transition between the first region R1and the second region R2. The stress profile of FIG. 2C also includesthe first and second regions R1 and R2 and the knee KN, and also showsthe depth of compression DOC extending from the substrate surface (z=0)into the second region R2. The refractive indices at the surface 22 ofthe substrate 20 due to the ion-exchange process for the TM and TEpolarizations respectively denoted n_(surf) ^(TM) and n_(surf) ^(TE).Note that the refractive index profiles n^(TM)(z) and n^(TE)(z) are theeffective indices associated with a waveguide defined by the spike SP inthe glass substrate 20.

The deeper second region R2 may be produced in practice prior to theshallower first region R1, or at the same time as the shallower region.The region R1 is adjacent substrate surface 22 and is relatively steepand shallow and defining the spike SP, whereas region R2 is less steepand extends relatively deep into the substrate to the aforementioneddepth D2 that is very large, and may be as deep as the middle of thesubstrate thickness. In an example, the region R1 has a maximumrefractive index n_(surf)=n₀ at substrate surface 22 and steeply tapersoff to an intermediate index n_(i), while region R2 tapers moregradually from the intermediate index down to the substrate (bulk)refractive index n_(s).

Usually in Li glasses, in the case of transverse magnetic (TM) waves,the indices n_(i) and n_(s) are about the same, while for TE waves n_(i)is lower than n_(s) because compressive stress at the knee lowers the TErefractive index relative to the TM one. The portion of the refractiveindex profiles n^(TM)(z) and n^(TE)(z) for region R1 represents thespike PS in the refractive index having a depth DOL_(sp)=DOL=D2. In anexample, the intermediate index n_(i) can be very close to the substraterefractive index n_(s), as shown in FIG. 2A by way of example.

Example Prism Coupling Apparatus and Mode Spectrum

Example prism-coupling systems suitable for use for carrying out themethods disclosed herein are also described in U.S. Patent ApplicationPublications No. 2014/0368808 and 2015/0066393, which are incorporatedby reference herein.

FIG. 3A is a schematic diagram of an example prism-coupling system 28that can be used to carry out aspects of the methods disclosed herein.The prism coupling methods using the prism-coupling system 28 arenon-destructive. This feature is particularly useful for measuringfrangible IOX articles 10 for research and development purposes and forQC in manufacturing.

The prism-coupling system 28 includes a support stage 30 configured tooperably support the IOX article 10. The prism-coupling system 28 alsoincludes a coupling prism 40 that has an input surface 42, a couplingsurface 44 and an output surface 46. The coupling prism 40 has arefractive index n_(p)>n₀. The coupling prism 40 is interfaced with theIOX article 10 being measured by bringing coupling-prism couplingsurface 44 and the surface 22 into optical contact, thereby defining aninterface 50 that in an example can include an interfacing (orindex-matching) fluid 52 having a thickness TH. In an example, theprism-coupling system 28 includes an interfacing fluid supply 53 fluidlyconnected to the interface 50 to supply the interfacing fluid 52 to theinterface. This configuration also allows for different interfacingfluids 52 with different refractive indices to be deployed. Thus, in anexample, the refractive index of the interfacing fluid 52 can be changedby operation of the interfacing fluid supply 53 to add a higher-index orlower-index interfacing fluid. In an example, the interfacing fluidsupply 53 is operably connected to and controlled by a controller 150.

In an exemplary measurement, a vacuum system 56 pneumatically connectedto the interface 50 can be used to control the thickness TH by changingthe amount of vacuum at the interface. In an example, the vacuum systemis operably connected to and controlled by the controller 150.

The prism-coupling system 28 includes input and output optical axes A1and A2 that respectively pass through the input and output surfaces 42and 46 of the coupling prism 40 to generally converge at the interface50 after accounting for refraction at the prism/air interfaces. Theprism-coupling system 28 includes, in order along the input optical axisA1, a light source 60 that emits measuring light 62 of wavelength λ, anoptional optical filter 66 that may be alternatively included in thedetector path on axis A2, an optional light-scattering element 70 thatforms scattered light 62S, and an optional focusing optical system 80that forms focused (measuring) light 62F, as explained below. Thus, inan example of the prism-coupling system 28, there are no opticalelements between light source 60 and prism input surface 42. Thecomponents from the light source 60 to the focusing optical system 80constitute an illumination system 82.

The prism-coupling system 28 also includes, in order along the outputoptical axis A2 from the coupling prism 40, a collection optical system90 having a focal plane 92 and a focal length f and that receivesreflected light 62R as explained below, a TM/TE polarizer 100, and aphotodetector system 130.

The input optical axis A1 defines the center of an input optical pathOP1 between the light source 60 and the coupling surface 44. The inputoptical axis A1 also defines a coupling angle θ with respect to thesurface 12 of the IOX article 10 being measured.

The output optical axis A2 defines the center of an output optical pathOP2 between the coupling surface 44 and the photodetector system 130.Note that the input and output optical axes A1 and A2 may be bent at theinput and output surfaces 42 and 46, respectively, due to refraction.They may also be broken into sub-paths by inserting minors (not shown)into the input and output optical paths OP1 and/or OP2.

In an example, the photodetector system 130 includes a detector (camera)110 and a frame grabber 120. In other embodiments discussed below, thephotodetector system 130 includes a CMOS or CCD camera. FIG. 3B is aclose-up elevated view of the TM/TE polarizer 100 and the detector 110of the photodetector system 130. In an example, the TM/TE polarizerincludes a TM section 100TM and a TE section 100TE. The photodetectorsystem 130 includes a photosensitive surface 112.

The photosensitive surface 112 resides in the focal plane 92 of thecollecting optical system 90, with the photosensitive surface beinggenerally perpendicular to the output optical axis A2. This serves toconvert the angular distribution of the reflected light 62R exiting thecoupling prism output surface 46 to a transverse spatial distribution oflight at the sensor plane of the camera 110. In an example embodiment,the photosensitive surface 112 comprises pixels, i.e., the detector 110is a digital detector, e.g., a digital camera. In an example, each pixelcan have a dimension of between 4 microns and 5 microns, e.g., 4.65microns

Splitting the photosensitive surface 112 into TE and TM sections 112TEand 112TM as shown in FIG. 3B allows for the simultaneous recording ofdigital images of the angular reflection spectrum (mode spectrum) 250,which includes the individual TE and TM mode spectra 250TE and 250TM forthe TE and TM polarizations of the reflected light 62R. Thissimultaneous detection eliminates a source of measurement noise thatcould arise from making the TE and TM measurements at different times,given that system parameters can drift with time.

FIG. 3C is a schematic representation of a mode spectrum 250 as capturedby the photodetector system 130. The mode spectrum 250 hastotal-internal-reflection (TIR) section 252 associated with guided modes252TE and 252TM and a non-TIR section 54 associated with radiation modesand leaky modes 254TE and 254TM. The transition between the TIR section52 and the non-TIR section 54 defines a critical angle for each of theTE and TM polarizations and is referred to as the TIR-PR transition. Thelocation of the TIR-PR transition for each polarization is referred toas the TIR-PR location.

The mode spectrum 250 includes both a TM mode spectrum 250TM and a TEmode spectrum 250TM. The TM mode spectrum 250TM includes mode lines orfringes 252TM while the TE mode spectrum 250TE includes mode lines orfringes 252TE. The mode lines or fringes 252TM and 252TE can either bebright lines or dark lines, depending on the configuration of theprism-coupling system 28. In FIG. 3C, the mode lines or fringes 252TMand 252TE are shown as dark lines for ease of illustration. In thediscussion below, the term “fringes” is also used as short-hand for themore formal term “mode lines.”

The stress characteristics can be calculated based on the difference inpositions of the TM and TE fringes 252TM and 252TE in the mode spectrum250. At least two fringes 252TM for the TM mode spectrum 250TM and atleast two fringes 252TE for the TE mode spectrum 250TE are needed tocalculate the surface stress CS. Additional fringes are needed tocalculate the stress profile CS(x), including the knee stress CSk.

With reference again to FIG. 3A, the prism-coupling system 28 includes acontroller 150, which is configured to control the operation of theprism-coupling system. The controller 150 is also configured to receiveand process from the photodetector system 130 image signals SIrepresentative of captured (detected) TE and TM mode spectra images. Thecontroller 150 includes a processor 152 and a memory unit (“memory”)154. The controller 150 may control the activation and operation of thelight source 60 via a light-source control signal SL, and receives andprocesses image signals SI from the photodetector system 130 (e.g., fromthe frame grabber 120, as shown). The controller 150 is programmable toperform the functions described herein, including the operation of theprism-coupling system 28 and the aforementioned signal processing of theimage signals SI to arrive at a measurement of one or more of theaforementioned stress characteristics of the IOX article 10.

FIG. 3D is another schematic representation of an example measured modespectrum 250 of an IOX article 10 formed using a Li-containing glasssubstrate 20 and an ion-exchange process using a mixture of NaNO₃ andKNO₃, with the mode spectrum including TM and TE spectra 250TM and 250TE(upper and lower portions, respectively) with respective mode lines252TM and 252TE. The TIR-PR transition is denoted for the TM modespecrum 250TM. The Li-containing glass was 196HLS having a fictivetemperature of 638° C. The glass was subjected to a Li+⇔K+, Na+ion-exchange process by placing the glass sample in a bath having 60 wt% KNO₃ and 40 wt % NaNO₃ at 390° C. for 3 hours.

As is known in the art, the fringes or mode lines 252TM and 252TE in themode spectrum can be used to calculate surface compression or“compressive stress” CS and depth of layer DOL associated with anion-exchange layer that forms an optical waveguide. In the presentexample, the mode spectrum 250 was obtained using a commerciallyavailable prism-coupling system, namely the FSM6000L surface stressmeter (“FSM system”), available from Luceo Co., Ltd. of Tokyo, Japan,which system is similar to the one described herein.

The measured values of CS and DOL for the example IOX article 10 were575 MPa and 4.5 microns, respectively. These are the parameters of theK+ enriched layer or spike region R1 adjacent the IOX article surface22. The auxiliary vertical dashed lines on the left-hand side of the TEand TM mode spectra 250TE and 250TM were added to FIG. 3D and showpositions in the spectra in which the aforementioned conventional FSMsystem assigns to correspond to the surface indices n_(surf) ^(TM) andn_(surf) ^(TE). The difference in these positions is proportional to thesurface stress or compressive stress CS. These positions are also usedin the calculation of the depth of layer or DOL.

In the mode spectrum 250 for a chemically strengthened Li-containingglass having undergone a Li+⇔K+, Na+ ion exchange, the position of thetransition from the bright to the dark portion of the spectrum (i.e.,the TIR-PR location) observed after the last fringe 52 in the spectrumthat corresponds to the highest-order guided mode, is shifted in the TEspectrum 250TE as compared to the TM spectrum 250M. These TIR-PRlocations for the TM and TE polarizations correspond to the effectiveindices at the knee KN, which are respectively denoted in FIG. 3D asn_(knee) ^(TM) and n_(knee) ^(TE) respectively. The effective indices atthe surface are denoted n_(surf) ^(TM) and n_(surf) ^(TE) for the TM andTE polarizations and are shown for reference (see also FIGS. 2A and 2B).

This shift in the location of the TIR-PR location (i.e., the location ofn_(knee) ^(TM) and n_(knee) ^(TE)) between the TE and TM spectra isproportional to the knee (compressive) stress CSk, i.e., the compressivestress CS at the knee KN, i.e., the depth at which the K+ concentrationin spike region R1 decreases approximately to the constant-levelconcentration originally in the substrate (e.g., the spatially constantconcentration in the glass matrix that makes up substrate body 21).

In the idealized mode spectra 250 of FIG. 3D, the TIR-PR transitions areshown as being infinitely sharp. With reference to the schematic diagramof an example TM mode spectrum 250TM of FIG. 3E, in practice, the TIR-PRlocations are defined by a gradual transition from light to dark, witheach transition having an intensity slope SLP, a width W_(TIR-PR) and alocation x′_(TIR-PR), each of which can vary due to experimental factorsand imperfections in the measurement system. For example, with referenceto FIGS. 3F and 3G, when a leaky mode 254L falls very close to theTIR-PR transition, it can affect the intensity distribution at theTIR-PR location so that the TIR-PR location x′_(TIR-PR) is shifted by anamount Δx′ from its original location to a shifted locationxs′_(TIR-PR), wherein the local coordinate x′ is shown. Note that thewidth W_(TIR-PR) can also be affected and is typically increased.

Mitigation of the main factors that adversely affect the accuratedetermination of the TIR-PR transitions for the TM and TE polarizationsto improve the measurement of the knee stress CSk are discussed below.

The measurements of the mode spectrum 250 of an IOX article 10 having anIOX region 24 defined by the K+ penetration of the IOX process, alongwith the TIR-PR locations for the TM and TE mode spectra 250TM and250TE, can be combined and used for effective QC of a family of stressprofiles that provide superior resistance to fracture. The spike regionR1 is relatively small in thickness when compared to the substratethickness T. For example, the spike region R1 may be 10 microns deep(i.e., DOL_(sp)=10 microns), while the substrate may be T=800 micronsthick. The profile of the spike SP may have a shape similar to acomplementary error function (erfc) shape, but may also be similar to alinear depth distribution, Gaussian depth distribution, or anotherdistribution. The main features of the spike SP are that it is arelatively shallow distribution and provides a substantial increase inthe surface compression over the level of compression at the bottom ofthe spike as defined by DOL_(sp).

FIG. 4 is an example plot of the compressive stress CS (MPa) versus anormalized position coordinate z/T, showing the model stress profile(solid) for an example chemically strengthened Li-containing glasssubstrate 20 that has undergone a K+ and Na+ IOX process. In the plot ofFIG. 4, the dashed line represents the model profile for Na+ diffusiononly (note that the model profile has the IOX process taking place attwo surfaces that respectively reside at z/T=−0.5 and +0.5). The exampleprofile has a parabolic deep portion or region R2 and the surface spikeregion R1 with spike SP.

In the present disclosure, the assumed convention is that compressivestress CS is positive and that tensile stress is negative. The modelprofile of FIG. 4 has a linear spike SP in region R1 added on top of adeep quadratic profile in region R2. Another feature of the spike SP isalso recognized from FIG. 4, namely that the typical slope of the stressdistribution in the spike R1 is significantly higher than the typicalslope in the deep portion R2 of the profile, which is assumed to followa power law, which in this specific example is parabolic (with powerp=2), for the purposes of making QC measurements.

FIG. 5A is a schematic representation of a measured mode spectrum 250showing the TE and TM mode spectra 250TE and 250TM based on actualmeasured mode spectra for an example chemically strengthenedLi-containing IOX article 10. Note again the offset in the x′ directionof the dark regions 254TM and 254TE. The TIR-PR locations for the TE andTM spectra are also shown and are offset relative to each other.

Assessing and Limiting the Adverse Effects of Sample Warpage

It has been found that non-flatness (warpage) of an IOX article 10 cansignificantly degrade the precision of the CSk measurement byintroducing random and systematic quasi-random errors in the detectedlocation of the TIR-PR transitions. This is particularly problematicbecause the amount of warpage that can adversely affect the knee stressmeasurement is not readily observable by the human eye. Thus, an aspectof the disclosure is a method for ensuring that an accuratedetermination of the knee stress can be made on a given glass samplethat could have an amount of (unseen) warp.

FIG. 5B is a schematic diagram that shows on the left side the TIR-PRtransition for a flat IOX article 10 and on the right side the TIR-PRtransition for a warped IOX article. A slope SLP of the TIR-PRtransition is denoted by the slanted dashed line. Note that the warpagemakes the TIR-PR transition less steep and more blurry (as indicatedschematically by the reduced contrast), which results in increaseduncertainty for the position of the maximum slope of the transition,which is normally assigned as the TIR-PR position.

Furthermore, it has been observed that warpage of the IOX article 10 canmake the intensity pattern of a leaky mode in the mode spectrum 250appear similar to the pattern of a guided mode, and vice versa,depending on the degree and orientation of the warp (convex or concave),and also depending on the position of the apex of the warped (e.g.,curved) glass surface relative to the center of the prism coupling area,and more specifically to the illuminated region of the coupling surface44 of the coupling prism 40. These effects lead to relatively largeerrors in detecting the TIR-PR location, which can lead to correspondingerrors in measurement of the knee stress CSk on the order of tens ofMPa.

An aspect of the methods disclosed herein tests for signatures of warpin the measured mode spectra 250. Signatures of warp include for examplea significantly smaller (less steep) slope of the light intensity forthe TIR-PR transition than is typical for flat samples, as illustratedin FIG. 5B. Another signature is a wider than expected spread in theTIR-PR transition, as indicated by the increased breadth of the curveformed by the derivative of the intensity profile (i.e., the derivativeof the angular distribution of intensity).

The tests for whether the level of warpage is acceptable may beperformed using measurements of the TIR-PR transition location for oneof the TM and TE mode spectra, or both the TM and the TE mode spectra.In the usual measurements of stress using the mode spectrum 250, the TMtransition is naturally sharper, especially for chemically-strengthenedLi-containing glasses. As such, the tests for whether the level ofwarpage in the sample is acceptable may be preferably restricted to theTIR-PR transition of the TM mode spectrum only.

It has been observed that a warped IOX article 10 also tends to broadenthe mode fringes 252TM and 252TE in the corresponding mode spectra 250TMand 250TE that correspond to guided or quasi-guided optical modes,especially with respect to the narrowest of these mode fringes. Acorollary of this broadening is also a reduction in the contrast ofthese fringes. Hence, to limit random and quasi-random errors resultingin part from sample warpage, the method utilizes measurements of thebreadth of selected narrowest fringes, or the peak slope of thederivative of the intensity profile across such fringes (e.g., the peakabsolute value of the second derivative), the fringe contrast, or anycombination thereof, and comparisons of the measured values to expectedacceptable standards based on modeling or previous measurements ofsamples with acceptable levels of warp.

In an example, any combination of the breadth, peak second derivative,and contrast of the intensity profile of the guided-mode TM fringehaving the closest effective index to that of the TM critical angle, andhigher effective index than that of the TM critical angle, can be usedfor testing whether the amount of warp in the sample is acceptable,i.e., that leads to a measurement of CSk having adequate accuracy.

Note that in some embodiments, the selected mode fringe for this testmay be simply the narrowest fringe in the given mode spectrum withoutregard for where it is relative to the critical angle (i.e., the TIR-PRtransition location) as even a crude estimate of the TIR-PR location maybe postponed for after the test which assesses whether the amount ofwarpage is acceptable.

In an example, the method conditions the mode spectra (signal) bystandard de-noising techniques, employing for example a LOESS algorithmand/or digital low-pass or band-pass filtering. The LOESS algorithm isdescribed in the article by W. S. Cleveland, “Robust locally weightedregression and smoothing scatterplots”, Journal of the Americanstatistical association, vol. 74, No. 368, pages 829-836 (December1979). De-noising of the signal is very helpful for reducing errors inthe decision routines caused by noise-induced large excursions of thederivatives of the signal. The bandwidth of the low-pass filter orband-pass filter is chosen such that filter-induced broadening of thenarrowest fringes in the spectra is appropriately smaller than thethreshold for rejecting a spectrum that is unacceptably broadened bywarp.

Thus, an aspect of the disclosure includes a method of improving ameasurement of knee stress in a chemically strengthened Li-containingglass sample (IOX article 10) having a warped surface and a body andthat includes an IOX region that defines a stress profile having a knee.The method comprises: capturing an image of at least one of a TE modespectrum and a TM mode spectrum; measuring a slope of light intensity ata transition between total-internal reflection and partial-internalreflection (TIR-PR) and measuring a width of the TIR-PR transition forat least one of the TE mode spectrum and TM mode spectrum; and comparingthe measured slope SLP and the measured width W_(TIR-PR) to a slope(steepness) threshold STH and a width threshold WT_(TIR-PR) associatedwith reference glass sample having a flat surface.

In an example reference glass sample is formed using the same IOXprocess used to form the warned glass sample.

In another example, the method includes: measuring a fringe width of oneof the narrowest TE mode fringe and the narrowest TM mode fringe; andcomparing the measured fringe width to a fringe width threshold asdefined by the reference glass sample, and only proceeding with thedetermining of the knee stress if the measured fringe width is as wideor smaller than the fringe width threshold.

Assessing and Limiting Adverse Effects of Illumination Non-Uniformities

Another imperfection that causes systematic and quasi-random errors inthe mode spectra relates to non-uniformities in the illumination used togenerate the mode spectra. An example of such illuminationnon-uniformity is a gradient in the angular illumination spectrum, and achanging orientation of the illuminating angular spectral distributionrelative to the mode spectra.

A significant gradient of the angular spectrum of the intensitydistribution can be produced by the combination of the light source 60,the coupling prism 40, and surrounding apertures of the prism couplingsystem used to capture images of the mode spectra. Illuminationnon-uniformities are particularly problematic when they are in thevicinity of the TIR-PR transition location and when there is anintensity gradient along the x′ direction as shown in FIGS. 3C, 3D and5A for example. This is because illumination non-uniformities can shiftthe TIR-PR transition location and fringe locations, and can result inan error in the direct CSk measurement when the shifts are not the samefor the TE and TM mode spectra. Another type of non-uniformity iscontamination of the detector array, which could result local darkeningof some pixels and interfere with the detection of the steepestintensity slope for determining the critical angle location.

Even if the gradient of illumination is the same in the vicinity of theTE and TM TIR-PR transition locations, the corresponding apparent shiftsof the critical angle can be different because slope of the TIR-PRtransition is different for the TE and the TM mode so that theirsensitivity to an illumination gradient is different.

An aspect of the disclosure is directed to methods of improving the CSkmeasurement by reducing the errors caused by illuminationnon-uniformities. In one example, a low-pass-filtered component of thesignal in the bright part of the reflected angular spectrum (the TIRregion) is analyzed and if it contains gradients greater than anacceptable upper limit, the controller 150 (via software) requires thatthe illumination gradients be fixed before taking measurements. This canbe done by adjusting the light source 60 or by adding an opticalgradient filter 66 in the light beam 62 from the light source 60.

Assessing and Mitigating the Adverse Effects of Leaky Modes

With reference again to FIGS. 3E through 3G, it has been recognized thatthe presence of a leaky mode (254L) in close proximity to the TIR-PRtransition location causes the intensity profile in the vicinity of thetransition to change significantly. This in turn can lead to significantsystematic errors, as well as quasi-random errors. Such errors cancombine with errors from other effects like moderate warp of the samplesor gradients in the illumination intensity, as discussed above. Thatsaid, the leaky mode issue by itself can be quite problematic because itcan shift the TIR-PR transition location (by Δx′ in FIG. 3G) and lead toerrors in the estimate of CSk that can be many tens of MPa, which isunacceptably large.

A leaky mode has an effective index that is lower than the lowest indexin the waveguide region (i.e., TIR section 252), which in our example,is lower than the refractive index at the bottom of the potassium spike(e.g., than the refractive index corresponding to the knee-point in theprofile). In this case, the light captured in this mode inside thewaveguide experiences some bouncing in the waveguide region (IOX region24) before leaking into the underlying portion of the body 21 of theglass substrate 20

A leaky mode 254L with an effective index close to the index of theTIR-PR transition tends to produce a coupling resonance in the vicinityof this transition and thus deforms the angular intensity distributionaround the TIR-PR transition location, as illustrated in FIGS. 3F and3G. This in turn causes a shift Δx′ in the location of the maximum slopeof the intensity distribution at the TIR-PR location relative to thetrue location associated with the critical angle. That is to say, aleaky mode 254L can cause a shift in the measured TIR-PR transitionlocation relative to its actual location measured in the absence of theleaky mode.

An aspect of the disclosure is directed to improving the measurement ofthe knee stress CSk by accounting for (i.e., compensating for) the shiftin the TIR-PR transition location due to a leaky mode 254L.

If the TIR-PR transition location can be established as usual, but thereis a broad resonance in the intensity distribution at a positioncorresponding to a lower effective index than the TIR-PR transition,then a correction for the shift in the position of the highest-slope isperform. The correction is calculated based on the distance between thelocation of the intensity extremum corresponding to the broad resonanceof the leaky mode and the measured raw position of the peak slope of theTIR-PR transition. This distance may be normalized to the distancebetween two highest-order modes in the same polarization state (TM orTE) for which the position of the transition is currently evaluated, orany combination of spacings of the guided modes in effective index, orcorresponding positions of their coupling resonances in angular space oron the measurement detector.

With a slow continuous increase in the depth D1 of the potassium ions inregion R1 of the profile (see FIG. 2), the effective index of the leakymode slowly increases, getting closer and closer to the effective indexof the TIR-PR transition. At the same time, the breadth of thecorresponding resonance in the mode spectra decreases, and the contrastof the corresponding spectral feature (mode fringe) increases. In thecase when the angular distribution of the light reflected from theprism-sample interface 50 is being detected and analyzed (i.e., in theform of a mode spectrum 250), the photodetector system 130 may beconfigured to collect reflected light 62R in a region where the modefringes corresponding to coupling resonances of guided modes are darkfringes. The resonance corresponding to the leaky mode is then alsodark, and its increased contrast upon approaching the TIR-PR transitionlocation also results in further lower light intensity (darkerresonance).

FIG. 5C is a schematic diagram of an example leaky mode resonance, i.e.,intensity distribution of the leaky mode. In an embodiment, a correctionfor the shift in the measured position of the critical angle (TIR-PRlocation) is calculated based a combination comprising measured valuesof the breadth BR of the resonance of the leaky mode (e.g., full-widthhalf maximum), a contrast of the resonance (intensity distribution) ofthe leaky mode based on I_(MAX) and I_(MIN) intensities (e.g., (e.g.,Contrast=[I_(MAX)−I_(MIN)]/[I_(MAX)+I_(MIN)]), a normalized intensity atthe intensity extremum of the leaky mode based on the I_(MAX) andI_(MAIN) intensities and spacing SX′ (in effective index, or acorresponding variable such as angular spacing, pixel spacing, ordistance on the detector) between the location x′_(LM) of the detectedextremum of the leaky mode and the raw position x′_(TIR-PR) of theTIR-PR transition peak slope. In some embodiments, the ratio ofnormalized intensity on the two sides of the leaky-mode resonance isalso used to calculate the correction.

Thus, an aspect of the methods disclosed herein includes a method ofcorrecting the shift of the TIR-PR location in either the TM modespectrum 250TM or both TM and TE mode spectra 250TM and 250TE due to thepresence of one or more nearby leaky modes 254L (TE, TM). Thiscorrection extends the range of profiles over which knee stressmeasurements can be made, i.e., it broadens the measurement window forwhich the knee stress CSk can be determined.

The TM and TE measurement sweet spots can be measured as a fractionalpart of the mode spacing, and in an example are normally each about 0.5modes wide. Since the TM and TE measurement sweet spots are offsetrelative to each other, the total measurement window is actuallynarrower, e.g., about 0.3 modes wide when considering both TM and TEmode spectra 250TM and 250TE.

With the correction made for the presence of a leaky move, themeasurement window for each of the TM and TE spectra can be about 0.9modes wide. If there is 0.2 mode shift between TM and TE spectra 250TMand 250TE, then the overall measurement window is 0.7 modes wide, whichrepresents a greater than 2× increase in the measurement window.

An example method of compensating for the presence of a leaky mode inthe calculation of the knee stress CSk is as follows:

-   -   1) Determine the position of maximum slope of the TIR-PR        transition for each of the TM and TE mode spectra.    -   2) Determine the leaky mode position from the TE and TM mode        spectra where the leaky mode is defined as a relative minimum        after the TIR-PR transition. In a specific example, the relative        minima are defined as normalized intensity minima of 6/255        (absolute units), occurring within 30 pixels.    -   3) Determine the TM and/or TE leaky mode correction amount in        either number-of-pixels, effective index, or angular space.    -   4) Determine the leaky mode width at half max.    -   5) Suppress the leaky mode correction if the leaky mode        correction is a greater distance than leaky mode offset.    -   6) Determine the final position of critical angle as the initial        maximum slope position+the leaky mode correction.    -   7) Correct for cases when the leaky mode is exactly at the        critical angle by shifting the critical angle to lower effective        index.    -   8) Correct for cases where TE has higher total mode count than        TM. This is caused by TE transition broadening due to warp.

Another aspect of the disclosure is directed to a method of improving ameasurement of knee stress in a chemically strengthened Li-containingglass sample having a surface and a body and that includes a stressprofile having a knee and that defines a waveguide that supports lightas guided waves and a leaky mode. The method comprises: capturing animage of a TE mode spectrum and a TM mode spectrum of the guide wavesand leaky mode; measuring a position of maximum slope of a transitionbetween a total-internal reflection and a partial-internal reflection(TIR-PR) for the light supported in the waveguide for each of the TEmode spectrum and the TM mode spectrum; determining from the TE and TMmode spectra a position of the leaky mode as a relative minima after theTIR-PR transition; determining from the leaky mode position an amount ofshift in the TIR-PR position caused by the leaky mode; adding the amountof shift from the measured position of the TIR-PR transition to arriveat a corrected TIR-PR transition location; and using the correctedTIR-PR transition location to determine the knee stress.

Other Approaches to Increasing the Size of the Measurement Window

The systems and methods described so far have allowed effectively toincrease the size of the measurement window or “sweet spot” formeasuring the knee stress CSk of an IOX article 10 by calculatingcorrections for the shift in the critical angle when the fractional partof the non-integer mode number (“fractional mode number”) of the spikein the polarization state under consideration (i.e., TE or TM) isgreater than about 0.65 and smaller than 1. As is known for directmeasurement of the knee stress CSk, the direct measurement of the TIR-PRtransition is relatively precise when the fractional mode number isbetween about 0.2 and 0.7, and more preferably is between about 0.3 and0.65.

Another aspect of the disclosure is directed to methods that correct fora shift in the TIR-PR transition location measured from the location ofthe peak slope of the transition when the distance from the last guidedmode to the peak-slope location corresponds to a fractional mode numberof between 0 and 0.2. In this case, the contribution to the shift in thepeak-slope location due to a leaky mode is not significant since theclosest leaky mode is quite far from the TIR-PR transition location. Theshift in the peak-slope location relative to the actual TIR-PRtransition location in this case is caused by the broadening of theresonance of the highest-order guided mode. This broadening is caused bythe limited resolution of the measurement system, the strength ofcoupling of the guided mode to the modes of propagation in the prism, aswell broadening due to (accepted) levels of warp in the measured IOXarticle, as discussed above.

The broadening of the resonance of the highest-order guided mode causesthe intensity distribution of the coupling resonance to overlap on oneside with the TIR-PR transition. This in turn causes the intensitydistribution of the resonance to be asymmetric and also causes a changein shape in the intensity distribution in the vicinity of the TIR-PRtransition, similar to what happens when a leaky mode is present. Thiscan cause the location of highest slope of the TIR-PR transition, whichis used as a surrogate for the location of the critical angle, to shiftas a result of the change in angular intensity distribution in the closeproximity of the TIR-PR transition. The amount of necessary correctioncan be determined by analyzing a large number of different spectra.

In one embodiment, the correction for the shift caused by the proximityof a leaky mode, and the correction for the shift caused by a closeproximity of a guided mode to the TIR-PR transition, are combined into asingle correction with a single mathematical expression or logical andmathematical expression, even though two separate causes for the shiftexist that normally don't operate simultaneously since only one or theother usually causes a shift.

In the above embodiments, the signature of a leaky mode in the measuredcoupling spectrum is substantially different from that of a guided mode,and a relatively straightforward method for detecting and distinguishingleaky modes from guided modes was implemented. In particular, theresonance for the leaky mode in this case is much broader than that ofnearby guided mode, and the contrast of the intensity profile of theleaky mode is much smaller than that of the guided modes.

In some cases the distance between a mode, guided or leaky, and thecritical angle is very small, less than about 0.15 of typical modespacing of the spike. In such cases it becomes much more difficult todistinguish between a guided mode and leaky mode based on only one ortwo parameters, such as breadth of the resonance and contrast of theresonance, as both these parameters have overlap in their correspondingranges observed for leaky and guided modes that are close to thecritical angle.

Furthermore, a guided mode may have enough broadening to have itsintensity on the lower-index side of the angular intensity distributionlowered significantly, making its intensity distribution very similar tothat of a leaky mode in the vicinity of the TIR-PR location. Then it maynot be clear whether the critical angle should be assigned to thesteepest slope on the high-index side of the resonance or on thelow-index side of the resonance, as it is not known whether theresonance belongs to a guided or leaky mode.

Furthermore, even when it is possible for a human to identify a featurein the intensity pattern that can help assign the resonance as leaky orguided, effects of warp and imperfect illumination can easily causeerrors in the assignment of such a questionable resonance as leaky orguided. In this case, a more sophisticated approach is preferred forassigning a resonance as leaky or guided when the location of the TIR-PRtransition is within the range of substantial effect of a nearbyresonance.

The assignment of a resonance as guided or leaky utilizes the breadth ofthe resonance, the contrast of the resonance, the difference inintensity distribution on either side of the resonance, the peak secondderivative in the resonance intensity profile, the breadth of thenearest TE or TM guided-mode resonance, the contrast of the nearest TEor TM guided-mode resonance, and the relative spacings of allresonances, including all guided-mode resonances having higher effectiveindex higher than the questionable resonance, and the spacing from thealready identified highest-order-mode resonance and the questionableresonance.

An example method uses the breadth of the resonance and the contrast ofthe resonance to identify and assign a resonance as “leaky” after theTIR-PR transition. The leaky mode position is determined from TE and TMmode spectra where the leaky mode is defined as a relative minimum afterthe TIR-PR transition. In a specific example, the relative minima aredefined as normalized intensity minima of 6/255 (abs units), occurringwithin 30 pixels.

Further, the example method can employ empirical additive corrections toshift the TIR-PR transition to account for leaky mode presence. In anexample, LW is defined as the leaky mode breadth (FWHM) and LO isdefined as the leaky mode position offset (px) from TIR-Pr transitionmaximum slope. A specific example of leaky mode correction for TM isdefined as: TM_Correction=−3.8·LW+61.1·(1/LO). A specific example ofleaky mode correction for TE is defined as:TE_Correction=10.6·LW+−31.2·(1/LO). The leaky mode correction is thenadded to the respective TM or TE TIR-PR transition location of maximumslope.

Improved CSk Measurement by Using High-Quality Mode Spectrum Images

The above-described methods can significantly increase the range ofapplicability of the direct CSk method by substantially reducing thesystematic error when any of the TIR-PR transitions (the TM or the TE)is not strictly inside a measurement sweet spot. The only cases whensignificant variability in the measurements of a sample occurs is onewhen a guided mode is located very close to the TIR-PR transition, e.g.,within less than about 0.05 mode spacings of the critical angle. In thiscase, it sometimes happens that the mode resonance contrast issignificantly decreased and the mode is not properly detected. Hence,the described new methods can be employed to increase (e.g., double) therange of conditions that can be measured using the direct CSk method.

In an example, the method can account for this near-integer total modecount in the TM spectrum 250TM by shifting the TIR-PR transition towardthe lower effective index space. In a specific example, when a TEspectrum contains a leaky mode and the TM spectrum does not appear tocontain a leaky mode (due to the above reduced resonance contrast), andTM fractional mode count is between 0.65 to 1.00, the TM TIR-PRtransition can be shifted toward lower index space by a select number ofpixels, e.g., 8 pixels, as determined empirically by analyzing hundredsof mode spectra.

Despite the improved precision and increased range of applicability ofthe above-described methods, the achieved precision of a single directCSk measurement may not be adequate in many cases for performing QC.Hence, another aspect of the present disclosure includes methods of QCthat have better precision.

In one embodiment, the quality of the mode spectra image is assessedbased on comparing the breadth of the narrowest coupling resonances toexpected reference values for assumed high-quality mode spectra images.A measurement is only accepted if the mode spectra image is deemed topass select criteria that define a high-quality mode spectra image.Further, the mode spectra images are captured at least twice, preferablythree times, and the sample position relative to the prism, or theillumination intensity or angular distribution is changed betweendifferent measurements, such that several (at least 2) raw values areobtained for the direct CSk and the reported value is the average of theat least two raw values.

An example method includes defining one or more standards for the imagequality of the captured mode spectra image(s) so that the knee stressCSk can be determined to within a precision of +/−15 MPa, +/−10 MPa, oreven +/−5 MPa. In an example, the method includes accurately measuringthe half-max intensity width of the mode fringes. This can includetaking into account the overshoot of the intensity on one side of thefringe that may be normalized by the overshoot of intensity on the otherside of the fringe, measuring the relative height of TM and TE intensityslope at the transition location (location of maximum slope), and thendetermining/assigning the TM and TE intensity slope at the transitionlocation (location of maximum slope).

In an example method, the image of the given TM or TE mode spectra 250TMor 250TE is deemed unacceptable for calculating the knee stress CSk if:

-   -   1) TE fringe overshoot >16/255 (abs units) AND TM intensity        slope >−25/255 (abs units) AND Average fringe width >8 (px) OR    -   2) TM intensity slope >−10/255 (abs units) AND Average fringe        width >8 (px) OR    -   3) TE fringe overshoot >30 (abs units) AND Average fringe        width >8 (px) OR    -   4) Average fringe width >40 (px)

Another aspect of the disclosure is a method of improving a measurementof a knee stress in a chemically strengthened Li-containing glass samplehaving a surface and a body and that includes a stress profile having aknee and that defines a waveguide that supports light as guided modes,comprising: capturing an image of a TE mode spectrum and a TM modespectrum; measuring a slope SLP of a transition between a total-internalreflection and a partial-internal reflection (TIR-PR) for the lightsupported by the waveguide for each of the TE mode spectrum and the TMmode spectrum; comparing the slope SLP to a steepness threshold STH andusing the slope to determine a location of the TIR-PR transition andusing the corrected TIR-PR transition location to determine the kneestress only if the slope SLP is greater (steeper) than the selectsteepness threshold.

Improved Measurement of CSk by Combining Direct and Indirect Methods

A further improvement in the precision in the measurement of the kneestress CSk is obtained by another embodiment of the present invention,where the accuracy of a well-implemented direct-CSk method is combinedwith the high precision of an indirect method such as the “birefringenceof the higher-order guided mode method” or BHOGM.

The direct CSk method uses the birefringence as determined from theoffset between the TM and TE TIR-PR transition locations (see e.g., FIG.3D) and the stress optic coefficient SOC for the material, e.g., via therelationship CSk=[n_(crit) ^(TE)−n_(crit) ^(TM)]/SOC, where n_(crit)^(TE) and n_(crit) ^(TM) are the values of the effective index at thecritical angle, i.e., at the TIR-PR transitions for the TE and TM modespectra 250TE and 250TM respectively.

As noted above, this method is improved to increase the measurementaccuracy and precision of the knee stress CSk by reducingnon-uniformities in the illumination, accounting for the presence ofleaky modes and their effect on the TIR-PR transition shape to correctthe intensity profile of the TIR-PR transition for shifts in thelocation of maximum slope.

The improved method utilizes several image characteristics of the modespectra 250 to correct the TIR-PR maximum slope location, which resultsin a much more precise calculation of the direct CSk. The mode spectraimage characteristics of interest include: the TIR transition width athalf maximum of the 1st derivative; the TIR-PR transition negative slopevalue at the minima; the intensity after transition, intensity at thetransition, intensity before transition, slope overshoot before andafter the transition; the offset of the TIR-PR transition due to leakymodes; the leaky mode sharpness evaluated through the breadth of theresonance; and the leaky mode intensity.

In this embodiment, advantage is taken of the fact that during QC mostsamples that pass in a sequence through a measurement system aresubstantially similar to their neighboring samples in the measurementsequence. This is because samples come in batches from IOX process runs,where most samples within a run are typically substantially identical.This allows for taking a running average of the directly measured kneestress CSk using multiple samples, where the precision of runningaverage is significantly better than the precision of a single directCSk measurement. The running average can be used to judge whether thevalues of indirect CSk obtained in the same sequence of measurements(mode spectra) are valid or not. For each sample, the indirect value ofCSk is assigned as the measured value of CSk. But this is onlyconsidered valid if one or more of the measured parameters (CS, DOL, theindirect CSk) are within an accepted pre-defined allowable deviation ofthe running average of the one or more parameters. In some cases, it mayalso be required that the direct CSk value for the same sample deviateby no more than a pre-defined allowable amount.

Furthermore, additional requirements for validity of the measurementscan include a requirement that the surface stress CS and the DOL of thespike SP be within pre-defined acceptable deviations from theircorresponding running averages, and that selected mode spacings orselected mode spacing ratios be within certain acceptable pre-defineddeviations of their corresponding running averages.

If a sudden large change is observed in the directly measured CSk, CS,DOL, the chosen mode spacings or the mode spacing ratios from thecorresponding running average, then it can be assumed that the sampledoes not belong to the same sequence, and additional measurements can betaken. A restart of the running average may also be triggered. Since thebenefit of the running average of previous samples is lost, in oneembodiment it can be required that only very high quality mode spectraimages be accepted for the restart with a direct CSk measurement. Thisleads to high-quality direct CSk measurements upon restart of therunning average. It may also be required that the CSk value assigned tothat restart sample be an average of two or more high-quality direct-CSkmeasurements for that sample.

While some low-quality mode spectra images may be acceptable formeasurements of samples that are deemed by the software to belong to thegroup that produced a running average, mode spectra images that do notmeet select quality standards may be rejected from participating in therunning average, with the goal of preserving the accuracy and improvedprecision of the running average for the CSk value.

The benefit of the high precision of the indirect method such as BHOGMis utilized most by such poor-quality mode spectra, for which the directCSk estimate would have quite poor precision. But the indirect BHOGMwill still typically have reasonably good precision, so that in anexample, the direct CSk is only used for determining whether the samplebelongs to the group for which the indirect CSk method produces a validvalue.

In a related embodiment, the running average is used not only to assigna sample as belonging to a group with a certain calibration for theindirect BHOGM, but also to dynamically change the calibration of theindirect BHOGM. As described above, when one or more of the measuredparameters of the sample (e.g., direct CSk, CS, DOL) are deemed outsidethe range of their correspondent running average, the running average isabandoned, and a new running average is started, preferably by imposinga requirement for higher-quality images, and multiple measurements onthe first or the first few samples of the new group.

Then a calibration factor for the BHOGM is calculated from the startednew running average of direct CSk, and the measured birefringence of thehighest-order guided mode, and said calibration factor is used to assignCSk values of subsequent samples based on their measured BHOGM and useof the calibration factor. The calibration factor is improved by formingits own running average, and the benefits of high-precision indirectmeasurements are reaped for the rest of the samples in the sequence thathave similar profiles as the samples that started the new runningaverage.

The indirect method of measuring the knee stress CSk uses the last modebirefringence (β_(x)) multiplied by a scaling factor (F₄) that iscalibrated for specific glass composition, the IOX process conditionsand the glass thickness.

CS _(k) ^(indirect)=β_(x) ·F ₄

The hybrid method uses the improved direct method to calibrate thescaling factor F₄ for various IOX process conditions for improvedaccuracy and a moving average of F₄ to mitigate variability of improveddirect CSk for improved precision. In addition to the moving average ofF₄, a moving average of the fringe spacing ratio, the compressive stressCS and DOL are saved (i.e., stored in memory in the controller 150). Inan example, a 15-point moving average is used in one example.

The flow diagram of FIG. 6 with steps S1 through S9 and followingdescription outline the basic calculation and software logic used tocarry out the hybrid method of determining CSk based on samplemeasurements, i.e., the measured mode spectra, which is the first stepS1 in the process. The present method, as with all of the methodsdisclosed herein, can be carried out in the controller 150 usingsoftware in the form of instructions embodied in a non-transitorycomputer-readable medium.

The second step S2 calculates the indirect CSk scaling factor F₄, whichas noted above, relates the improved direct CSk with the last modebirefringence (β_(x)):

$F_{4}^{instant} = \frac{{CS}_{k}^{direct}}{\beta_{x}}$

The third step S3 determines if a re-calibration is needed. Ifself-recalibration is needed, then the moving averages are deleted instep S4 and a new moving average is started start over. The criteria forthis decision-making step can include one or more of the following. Thethresholds below are one example implementation.

-   -   1) TM(0,1,2) fringe spacing ratio differs from the moving        average by more than 0.07 (2nd step only);    -   2) TM(0,1) fringe spacing differs from the moving average by        more than 14 px (1st step only);    -   3) CS differs from the moving average by more than 70 Mpa;    -   4) DOL differs from the moving average by more than 0.7 μm;    -   5) CS differs from the moving average by more than 35 Mpa AND        DOL differs from the moving average by more than 0.35 μm;    -   6) Leaky mode state changes (e.g., moving average has no leaky        modes, new measurement has leaky mode or vice versa);    -   7) Recipe code changes in the software;    -   8) A change in the conditions of the IOX process (e.g., K, Na        bath concentrations, diffusion temperature, etc.).

If no re-calibration is needed, then the fifth step S5 involves checkingthe image quality of the mode spectra based on select image-qualitycriteria, which in an example can include one or more of the following:

-   -   1) The TIR transition gradient ≤−30 (transition slope must be        steep);    -   2) Average mode width at intensity half max ≤10 pixels;    -   3) Average mode overshoot ≤25 (i.e., white area after modes must        be non-existent or very low intensity).

If the image quality is deemed to be “good,” then the sixth step S6involves updating the moving average, which includes adding F₄^(instant) to a moving average F₄ array to establish a moving average F₄^(average). If the image quality is “bad,” then the method proceeds tostep S7, which inquires whether the array has fewer than 3 data points.If “yes,” then the method proceeds to step S8 which cancels themeasurement, has the controller issue an error message and sends themethod back to step Si to force a re-measurement of the IOX article(sample). If the image quality is bad and the array has greater than 2data points, then the method measures the knee stress CSk^(hybrid) ofthe sample per the last step S9 but does not add F₄ ^(instant) to the F₄moving average array (i.e., to the moving average F₄ ^(average)), i.e.,the method skips the sixth step S6.

For a good mode spectrum image per step 5, then once step S6 is carriedout, the method proceeds to step S9 where the hybrid knee stress iscalculated via the equation: CSk^(hybrid)=β_(x)·F₄ ^(average). Thishybrid calculation of the knee stress CSk^(hybrid) can result in anaccuracy that is within +/−15 MPa and a precision within +/−3 MPa for asufficient number of samples, e.g., 3 or more samples and preferably 5or more samples or even 10 or more samples.

Another aspect of the disclosure is a method of measuring a knee stressCSk in chemically strengthened Li-containing glass samples each having asurface and a body and that includes a stress profile having a knee andthat defines a waveguide that supports light as guided modes in spikeregion which has a monotonically decreasing index profile. The methodcomprises: measuring TE and TM mode spectra for each of the multipleglass samples; for each of the measured TE and TM mode spectra, directlymeasuring a knee stress CSk^(direct) and also indirectly measuring theknee stress via CSk^(indirect)=β_(x)·F₄, where β_(x) is a last-modebirefringence and F₄ is a scaling factor; calculating a moving averageF₄ ^(average) for the scaling factor F₄ using the directly measured kneestresses CSk^(direct) via the relationship F₄=CSk^(direct)/β_(x); andcalculating a hybrid knee stress CSk^(hybrid)=β_(x)·F₄ ^(average).

QC Methods

Aspects of the disclosure are directed to QC methods of forming the IOXarticle (glass sample) 10 as disclosed herein.

An example QC method is directed to performing QC of an ion-exchange(IOX) process used to form chemically strengthened Li-containing glasssamples 10. The first step in the method includes, for each of aplurality of glass samples formed by the IOX process, measuring the TEand TM mode spectra 250TE and 250TM of the guided modes for each of theglass samples. The next step involves comparing the measured TE and TMmode spectra to reference TE and TM mode spectra of at least onereference glass sample formed using the same IOX process. In an example,the reference samples all have flat surfaces to avoid measurementerrors. The next step includes adjusting one or more of the IOX processparameters to maintain the measured TE and TM mode spectra to be withinat least one mode spectrum tolerance of the reference TE and TM modespectra. Example IOX process parameters include: the concentration ofthe in-diffusing ions (e.g., K+ and Na+), the diffusion temperature andthe diffusion time.

The QC methods can also include comparing the TIR-PR transition slopesof the measured samples to those of the reference samples. In this case,the at the least one mode spectrum tolerance comprises the referenceslopes, wherein the measured slopes are at least as steep as thereference slopes.

The QC methods can also include comparing the widths of the TM and/or TEfringes 252TM and 252TE of the measured mode spectra to the widths ofthe TM and/or TE of the reference mode spectra. In this case, the atleast one mode spectrum tolerance comprises the reference widths,wherein the measured reference widths are the same size or smaller thanthe reference widths to indicate that the IOX process is satisfactory.Measured fringe widths greater than the reference fringe widthsnecessitate making one or more adjustments to the IOX process.

In an example, the QC methods can include determining a knee stress CSkfor each glass sample, and then comparing the determined knee stress toa tolerance range on the knee stress and adjusting the IOX process whenthe determined knee stress falls outside of the tolerance range. In anexample, the knee stress tolerance range can be determined frommeasuring the knee stress of multiple reference glass samples. In oneexample, the knee stress tolerance range is 70 Mpa while in anotherexample is 50 Mpa.

As part of the QC method, the knee stress can be determined “directly”by calculating

CSk=[n _(crit) ^(TE) −n _(crit) ^(TM)]/SOC,

where as noted above, n_(crit) ^(TE) and n_(crit) ^(TE) are respectivevalues of the critical-angle effective index at the TIR-PR transitionsfor the measured TE and TM mode spectra.

Another example of the method includes using the above-described hybridcalculation of the knee stress that uses both a direct and indirect kneestress calculation.

In an aspect 1, a method of ensuring an accurate measurement of kneestress in a chemically strengthened Li-containing glass sample having awarped surface comprises: capturing a TE mode spectrum and a TM modespectrum of the glass sample; measuring a TIR-PR slope of lightintensity at a TIR-PR transition between a total-internal reflection(TIR) section and a partial-internal reflection (PR) section for one ofthe TE mode spectrum and TM mode spectrum; measuring a TIR-PR width ofthe TIR-PR transition for at least one of the TE mode spectrum and TMmode spectrum; comparing the measured TIR-PR slope to a TIR-PR slopethreshold and the measured TIR-PR width to a TIR-PR width threshold,wherein the TIR-PR slope threshold and the TIR-PR width threshold aredefined by a reference glass sample having a flat surface; and using theTE mode spectrum and the TM mode spectrum to determine the knee stressonly if the measured TIR-PR slope is greater than the TIR-PR slopethreshold and the measured TIR-PR width is less than the TIR-PR widththreshold.

An aspect 2 according to aspect 1, further comprising: forming the glasssample using an ion-exchange (IOX) process that exchanges K+ and Na+ forLi in the Li-containing glass sample to define a spike region and a deepregion that define the knee stress; and forming the reference glasssample using the same IOX process as used in forming the glass sample.

An aspect 3 according to aspect 1 or 2, wherein the TE mode spectrumcomprises TE mode fringes with a narrowest TE mode fringe and the TMmode spectrum comprises TM mode fringes with a narrowest TM mode fringe,and further comprising: measuring a fringe width of one of the narrowestTE mode fringe and the narrowest TM mode fringe; comparing the measuredfringe width to a fringe width threshold as defined by the referenceglass sample; and proceeding with the determining of the knee stressonly if the measured fringe width is smaller than the fringe widththreshold.

An aspect 4 according to any preceding aspect, wherein the TE modespectrum comprises TE mode fringes with a narrowest TE mode fringe andthe TM mode spectrum comprises TM mode fringes with a narrowest TM modefringe, and further comprising: measuring a contrast of one of thenarrowest TE mode fringe and TM mode fringes; and comparing the measuredcontrast to a contrast threshold as defined by the reference glasssample; and proceeding with the determining of the knee stress if themeasured contrast is greater than the contrast threshold.

An aspect 5 according to any preceding aspect, wherein the TE modespectrum comprises TE mode fringes with a narrowest TE mode fringe andthe TM mode spectrum comprises TM mode fringes with a narrowest TM modefringe, and further comprising: measuring an intensity profile of one ofthe narrowest TE mode fringe and TM mode fringes; determining anabsolute value of a second derivative of the measured intensity profile;and comparing the absolute value of a second derivative to secondderivative threshold as defined by the reference glass sample; andproceeding with the determining of the knee stress if the measuredabsolute value of a second derivative is greater than the secondderivative threshold.

An aspect 6 according to any one of aspect 3 through 5, wherein thenarrowest TE mode fringe and the narrowest TM mode fringe are theclosest of the TE and TM mode fringes to the TIR-PR transition.

An aspect 7 according to any preceding aspect, wherein the capturing ofthe TE mode spectrum and a TM mode spectrum of the glass sample isperformed using a prism-coupling system.

An aspect 8 according to any preceding aspect, wherein the determiningof the knee stress CSk comprises using the relationship CSk=[n_(crit)^(TE)−n_(crit) ^(TM)]/SOC, where n_(crit) ^(TE) and n_(crit) ^(TE) arerespective values of the critical-angle effective index at the TIR-PRtransitions for the TE and TM mode spectra.

In an aspect 9, a method of measuring knee stress in a chemicallystrengthened Li-containing glass sample having a surface and a body andthat includes a stress profile having a knee and that defines awaveguide that supports light as guided waves and a leaky mode comprisescapturing a TE mode spectrum and a TM mode spectrum of the guide wavesand the leaky mode, wherein each mode spectrum has a total internalreflection (TIR) section and a partial-internal reflection (PR) betweenwhich resides a TIR-PR transition with a TIR transition location;determining respective TIR-PR transition locations for the TE and TMmode spectra; determining from the TE and TM mode spectra a position ofthe leaky mode relative to the TIR-PR transitions for the TE and TM modespectra; determining from the leaky mode position an amount of shift inthe TIR-PR position for each of the TM and TE mode spectra as caused bythe leaky mode; adding the amount of shift from the measured position ofthe TIR-PR transition to arrive at a corrected TIR-PR transitionlocation for each of the TM and TE mode spectra; and using the correctedTIR-PR transition locations of the TM and TE mode spectra to determinethe knee stress.

An aspect 10 according to aspect 9, wherein the TIR-PR transition isdefined by a TIR-PR transition intensity profile, the leaky mode has aleaky mode intensity profile, and wherein the determining of the amountof shift in the TIR-PR position caused by the leaky mode comprisessubtracting the leaky mode intensity profile from the TIR-PR transitionintensity profile to define a corrected TIR-PR position of the TIR-PRtransition.

An aspect 11 according to aspect 10, further comprising characterizingthe leaky mode intensity profile by: measuring a breadth of the leakymode intensity profile; measuring a contrast of the leaky mode intensityprofile; and measuring a spacing between the leaky mode and the TIR-PRtransition;

An aspect 12 according to aspect 11, wherein determining the position ofthe leaky mode includes measuring a relative intensity minimum in thepartial-internal reflection section and adjacent the TIR-PR transition.

An aspect 13 according to aspect 12, wherein the leaky mode has anintensity profile defined using a digital intensity scale from 0 to 255using a digital sensor having pixels, and wherein the intensity minimais 6/255 or less and falls within 30 pixels of the TIR-PR transition.

An aspect 14 according to aspect 13, wherein each pixel has a size ofbetween 4 microns and 5 microns.

An aspect 15 according to any one of aspect 12 through 14, wherein thedetermining of the knee stress CSk comprises using the relationshipCSk=[n_(crit) ^(TE)−n_(crit) ^(TM)]/SOC, where n_(crit) ^(TE) andn_(crit) ^(TE) are respective values of the critical-angle effectiveindex at the TIR-PR transitions for the TE and TM mode spectra.

In an aspect 16, a method of ensuring an accurate measurement of kneestress in a chemically strengthened Li-containing glass sample having asurface and a body and that includes a stress profile having a knee andthat defines a waveguide that supports light as guided modes comprises:capturing TE mode spectrum and a TM mode spectrum respectivelycomprising TE fringes and TM fringes; measuring a slope SLP of atransition between a total-internal reflection and a partial-internalreflection (TIR-PR) for the light supported by the waveguide for each ofthe TE mode spectrum and the TM mode spectrum; and comparing the slopeto a steepness threshold STH and using the slope to determine a locationof the TIR-PR transition and using the corrected TIR-PR transitionlocation to determine the knee stress only if the slope is greater thanthe select steepness threshold STH.

An aspect 17 according to aspect 16, wherein the select steepnessthreshold STH is defined by measuring mode spectra of a reference glasssample for which an acceptable measurement of the knee stress wasobtained.

An aspect 18 according to aspect 16 or 17, wherein the knee stressmeasurement has a knee stress measurement error, and wherein thesteepness threshold STH is selected such the knee stress measurementerror is determined to within +/−15 MPa.

An aspect 19 according to aspect 18, wherein the steepness threshold STHis selected such that the knee stress measurement error is within +/−10MPa.

An aspect 20 according to aspect 19, wherein the steepness threshold STHis selected such that the knee stress measurement error within +/−5 MPa.

An aspect 21 according to any of aspects 16 through 20, wherein eachTIR-PR transition has an intensity profile wherein measuring the slopeSLP for each of the TIR-PR transition regions for the TE mode spectrumand the TM mode spectrum comprises determining a location of thehalf-maximum intensity of the TIR-PR transition intensity profile andmeasuring the slope SLP at the location of the half-maximum intensity ofthe TIR-PR transition intensity profile.

An aspect 22 according to aspect 21, wherein the TIR-PR transitiondefines a boundary between a TIR section and a PR section of the givenTE or TM mode spectrum, and further comprising performing a best fit tothe TIR-PR transition intensity profile that omits an overshoot of theintensity on the TIR side of the TIR-PR transition.

An aspect 23 according to aspect 21 or 22, wherein the TIR-PR transitionintensity profile is measured on a digital intensity scale of 0 to 255units, and wherein the steepness threshold STH=−25/255 as measured onthe digital intensity scale.

An aspect 24 according to aspect 21 or 22, wherein the TIR-PR transitionintensity profile is measured on a digital intensity scale of 0 to 255units, and wherein the steepness threshold STH=−10/255 as measured onthe digital intensity scale.

An aspect 25 according to any of aspects 21-24, wherein the TIR-PRtransition intensity profile is measured on a digital intensity scale of0 to 255 units, wherein TIR-PR transition defines a boundary between aTIR section and a PR section of the given TE or TM mode spectrum,wherein the TIR-PR transition has an intensity overshoot on the TIRside, and wherein the measurement of the knee stress proceeds only ifthe intensity overshoot is less than an overshoot tolerance of 30/255 asmeasured on the digital intensity scale.

An aspect 26 according to aspect 25, wherein the overshoot tolerance is16/255 as measured on the digital intensity scale.

An aspect 27 according to any of aspects 16-26, further comprisingmeasuring a first width of at least one TE fringe and a second width ofat least one TM fringe and proceeding with determining the knee stressfrom the TE mode spectrum and the TM mode spectrum only if the first andsecond measured widths are within a select width tolerance.

An aspect 28 according to aspect 27, wherein the width tolerance isdefined by measured widths of TE and TM reference fringes of referencemode spectra of a reference glass sample for which an acceptablemeasurement of the knee stress was obtained.

An aspect 29 according to aspect 27 or 28, wherein TE and TM fringes aremeasured on a digital intensity scale of 0 to 255 units using a sensorhaving an array of pixels, and proceeding with determining the kneestress from the TE mode spectrum and the TM mode spectrum only if firstand second widths are each smaller than 40 pixels.

An aspect 30 according to aspect 29, wherein each pixel has a dimensionof between 4 microns and 5 microns.

An aspect 31 according to aspect 27 or 28, wherein TE and TM fringes aremeasured on a digital intensity scale of 0 to 255 units using a sensorhaving an array of pixels, and proceeding with determining the kneestress from the TE mode spectrum and the TM mode spectrum only if firstand second widths are each smaller than 8 pixels.

An aspect 32 according to aspect 31, wherein each pixel has a dimensionof between 4 microns and 5 microns.

An aspect 33 according to any of aspects 27-32, wherein: measuring thefirst width of at least one TE fringe comprising measuring first widthsof multiple TE fringes and defining an average first width; measuringthe second width of at least one TM fringe comprising measuring firstwidths of multiple TM fringes and defining an average second width; andcomparing the average first width and the average second width to theselect width tolerance.

An aspect 34 according to aspect 33, wherein TE and TM fringes aremeasured on a digital intensity scale of 0 to 255 units using a sensorhaving an array of pixels, and proceeding with determining the kneestress from the TE mode spectrum and the TM mode spectrum only if firstand second average widths are each smaller than 40 pixels.

An aspect 35 according to aspect 33, wherein TE and TM fringes aremeasured on a digital intensity scale of 0 to 255 units using a sensorhaving an array of pixels, and proceeding with determining the kneestress from the TE mode spectrum and the TM mode spectrum only if firstand second average widths are each smaller than 8 pixels.

An aspect 36 according to aspect 35, wherein each pixel has a dimensionof between 4 microns and 5 microns.

An aspect 37 according to any of aspects 16 through 36, wherein thedetermining of the knee stress CSk comprises using the relationshipCSk=[n_(crit) ^(TE)−n_(crit) ^(TM)]/SOC, where n_(crit) ^(TE) andn_(crit) ^(TE) are respective values of the critical-angle effectiveindex at the TIR-PR transitions for the TE and TM mode spectra.

In an aspect 38, a method of measuring a knee stress in chemicallystrengthened Li-containing glass samples each having a surface and abody and that includes a stress profile having a knee and that defines awaveguide that supports light as guided modes in the spike region whichhas a monotonically decreasing index profile comprises: measuring TE andTM mode spectra for each of the multiple glass samples; making a directmeasurement of the knee stress using the TE and TM mode spectra; makingan indirect measurement of the knee stress that employs the directmeasurements of the knee stress to define a moving-averaged scalingfactor for the indirect measurement; and calculating a hybrid value forthe knee stress that using the moving-averaged scaling factor and abirefringence measurement for the sample.

In an aspect 39, a method of measuring a knee stress in chemicallystrengthened Li-containing glass samples each having a surface and abody and that includes a stress profile having a knee and that defines awaveguide that supports light as guided modes in the spike region whichhas a monotonically decreasing index profile comprises: measuring TE andTM mode spectra for each of the multiple glass samples, wherein the TEand TM mode spectra have respective TE and TM fringes and respectivetotal-internal reflection and a partial-internal reflection (TIR-PR)transitions associated with a critical angle and that define respectivecritical angle effective index values n_(crit) ^(TE) and n_(crit) ^(TM);for each of the measured TE and TM mode spectra, directly measuring aknee stress CSk^(direct) and also indirectly measuring the knee stressvia CSk^(indirect)=β_(x)·F₄, where β_(x) is a last-mode birefringenceand F₄ is a scaling factor; calculating a moving average F₄ ^(average)for the scaling factor F₄ using the directly measured knee stressesCSk^(direct) for the multiple samples via the relationshipF₄=CSk^(direct)/β_(x); and calculating a hybrid knee stressCSk^(hybrid)=β_(x)·F₄ ^(average)

An aspect 40 according to aspect 39, wherein directly measuring the kneestress CSk^(direct) is performed using the relationshipCSk^(direct)=[n_(crit) ^(TE)−n_(crit) ^(TM)]/SOC.

An aspect 41 according to aspect 39 or 40, wherein the moving averageincludes greater than three values of the scaling factor F₄.

An aspect 42 according to any of aspects 39 through 41, furthercomprising measuring a spacing between adjacent TM fringes and startinga new moving average if the spacing exceeds a fringe spacing tolerance.

An aspect 43 according to any of aspects 39 through 42, furthercomprising determining a depth of layer DOL for each glass sample,calculating a moving average of the depth of layer DOL, and starting anew moving average of the depth of layer DOL and for the moving averageF₄ ^(average) for the scaling factor F₄ if a measured depth of layer DOLdiffers from the moving average of the depth of layer DOL by more than0.7 microns.

In an aspect 44, a method of ensuring an accurate measurement of kneestress in a chemically strengthened Li-containing glass sample having asurface and a body and that includes a stress profile having a knee andthat defines a waveguide that supports light as guided modes comprises:irradiating the glass sample by directing light from a light source as alight beam through a coupling prism and to the surface of the sample togenerate an angular illumination spectrum; detecting the angularillumination spectrum at a digital sensor to capture TE mode spectrumand a TM mode spectrum respectively comprising TE fringes and TM fringesand respective total-internal reflection and a partial-internalreflection (TIR-PR) transitions associated with a critical angle andthat define respective critical angle effective index values n_(crit)^(TE) and n_(crit) ^(TM), measuring an intensity gradient in the angularillumination spectrum in the vicinity of the TIR-PR transitions; andproceeding with the measurement of the knee stress only if the measuredintensity gradient is less than an intensity gradient threshold.

An aspect 45 according to aspect 44, wherein the intensity gradientthreshold is determined by measuring an intensity gradient fromreference glass sample for which an acceptable measurement of the kneestress was obtained.

An aspect 46 according to aspect 44 or 45, further comprising correctingthe intensity gradient to fall within the intensity gradient thresholdby adjusting the irradiation of the glass sample.

An aspect 47 according to aspect 46, wherein said correcting comprisesinserting a gradient optical filter in the light beam.

An aspect 48 according to any of aspects 44 through 47, wherein themeasuring of the intensity gradient is performed by comparing anintensity distribution of the TE and TM mode spectra as detected by thedigital sensor to a reference intensity.

An aspect 49 according to any of aspects 44 through 48, wherein thedetermining of the knee stress CSk comprises using the relationshipCSk=[n_(crit) ^(TE)−n_(crit) ^(TM)]/SOC.

In an aspect 50, a method of performing quality control of anion-exchange (IOX) process used to form chemically strengthenedLi-containing glass samples having a surface and a body and thatincludes a stress profile having a spike and a knee and that defines awaveguide that supports light as guided modes comprises: for each of aplurality of glass samples formed by the IOX process, measuring TE andTM mode spectra of the guided modes for each of the glass samples;comparing the measured TE and TM mode spectra to reference TE and TMmode spectra of at least one reference glass sample formed using thesame IOX process and having a flat surface; and adjusting the IOXprocess to maintain the measured TE and TM mode spectra to be within atleast one mode spectrum tolerance of the reference TE and TM modespectra.

An aspect 51 according to aspect 50, wherein the measured TE and TM modespectrum comprise total-internal reflection and a partial-internalreflection (TIR-PR) transitions having respective slopes, wherein thereference TE and TM mode spectrum comprise TIR-PIR transitions havingrespective slopes, and wherein at the least one mode spectrum tolerancecomprises the reference slopes, wherein the measured slopes are at leastas steep as the reference slopes.

An aspect 52 according to aspect 50 or 51, wherein adjusting the IOXprocess includes first and second in-diffusing ions, and includes atleast one of: adjusting at least one of a first concentration of thefirst in-diffusing ion and a second concentration of the secondin-diffusing ion; adjusting a diffusion temperature; and adjusting asdiffusion time.

An aspect 53 according to any of aspects 50 through 52, wherein thefirst and second in-diffusing ions are K+ and Na+ and are exchanged forLi+ ions in the glass sample.

An aspect 54 according to any of aspects 50 through 53, wherein themeasured TE and TM mode spectra comprise respective measured TE and TMmode fringes having respective measured widths, the reference TE and TMmode spectra comprise respective reference TE and TM mode fringes havingrespective reference widths, and wherein at the least one mode spectrumtolerance comprises the reference widths, wherein the measured referencewidths are the same size or smaller than the reference widths.

An aspect 55 according to any of aspects 50 through 54, furthercomprising: determining a knee stress CSk for each glass sample; andcomparing the determined knee stress to tolerance range on the kneestress and adjusting the IOX process when the determined knee stressfalls outside of the tolerance range.

An aspect 56 according to aspect 55, wherein the knee stress tolerancerange is determined from measuring the knee stress of multiple referenceglass samples.

An aspect 57 according to aspect 56, wherein the knee stress tolerancerange is 70 Mpa.

An aspect 58 according to aspect 56, wherein the knee stress tolerancerange is 50 Mpa.

An aspect 59 according to any of aspects 55-58, wherein the determiningof the knee stress CSk comprises calculating CSk=[n_(crit)^(TE)−n_(crit) ^(TM)]/SOC, where n_(crit) ^(TE) and n_(crit) ^(TE) arerespective values of the critical-angle effective index at the TIR-PRtransitions for the TE and TM mode spectra.

An aspect 60 according to any of aspects 55-58, wherein the knee stressCSk for each glass sample comprises: directly measuring a knee stressCSk^(direct)=[n_(crit) ^(TE)−n_(crit) ^(TM)]/SOC, where n_(crit) ^(TE)and n_(crit) ^(TE) are respective values of the critical-angle effectiveindex at the TIR-PR transitions for the TE and TM mode spectra;indirectly measuring the knee stress via CSk^(indirect)=β_(x)·F₄, whereβ_(x) is a last-mode birefringence and F₄ is a scaling factor;calculating a moving average F₄ ^(average) for the scaling factor F₄using the directly measured knee stresses CSk^(direct) for the multiplesamples via the relationship F₄=CSk^(direct)/β_(x); and calculating ahybrid knee stress CSk=CSk^(hybrid)=β_(x)·H₄ ^(average).

It will be apparent to those skilled in the art that variousmodifications to the preferred embodiments of the disclosure asdescribed herein can be made without departing from the spirit or scopeof the disclosure as defined in the appended claims. Thus, thedisclosure covers the modifications and variations provided they comewithin the scope of the appended claims and the equivalents thereto.

What is claimed is:
 1. A method of measuring knee stress in a chemicallystrengthened Li-containing glass sample having a warped surface,comprising: capturing a TE mode spectrum and a TM mode spectrum of theglass sample; measuring a TIR-PR slope of light intensity at a TIR-PRtransition between a total-internal reflection (TIR) section and apartial-internal reflection (PR) section for one of the TE mode spectrumand TM mode spectrum; measuring a TIR-PR width of the TIR-PR transitionfor at least one of the TE mode spectrum and TM mode spectrum; comparingthe measured TIR-PR slope to a TIR-PR slope threshold and the measuredTIR-PR width to a TIR-PR width threshold, wherein the TIR-PR slopethreshold and the TIR-PR width threshold are defined by a referenceglass sample having a flat surface; and using the TE mode spectrum andthe TM mode spectrum to determine the knee stress if the measured TIR-PRslope is greater than the TIR-PR slope threshold and the measured TIR-PRwidth is less than the TIR-PR width threshold.
 2. The method accordingto claim 1, further comprising: forming the glass sample using anion-exchange (IOX) process that exchanges K+ and Na+ for Li in theLi-containing glass sample to define a spike region and a deep regionthat define the knee stress; and forming the reference glass sampleusing the same IOX process as used in forming the glass sample.
 3. Themethod according to claim 1, wherein the TE mode spectrum comprises TEmode fringes with a narrowest TE mode fringe and the TM mode spectrumcomprises TM mode fringes with a narrowest TM mode fringe, and furthercomprising: measuring a fringe width of one of the narrowest TE modefringe and the narrowest TM mode fringe; comparing the measured fringewidth to a fringe width threshold as defined by the reference glasssample; and proceeding with the determining of the knee stress only ifthe measured fringe width is smaller than the fringe width threshold. 4.The method according to claim 1, wherein the TE mode spectrum comprisesTE mode fringes with a narrowest TE mode fringe and the TM mode spectrumcomprises TM mode fringes with a narrowest TM mode fringe, and furthercomprising: measuring a contrast of one of the narrowest TE mode fringeand TM mode fringes; and comparing the measured contrast to a contrastthreshold as defined by the reference glass sample; and proceeding withthe determining of the knee stress if the measured contrast is greaterthan the contrast threshold.
 5. The method according to claim 1, whereinthe TE mode spectrum comprises TE mode fringes with a narrowest TE modefringe and the TM mode spectrum comprises TM mode fringes with anarrowest TM mode fringe, and further comprising: measuring an intensityprofile of one of the narrowest TE mode fringe and TM mode fringes;determining an absolute value of a second derivative of the measuredintensity profile; and comparing the absolute value of a secondderivative to second derivative threshold as defined by the referenceglass sample; and proceeding with the determining of the knee stress ifthe measured absolute value of a second derivative is greater than thesecond derivative threshold.
 6. The method according to claim 3, whereinthe narrowest TE mode fringe and the narrowest TM mode fringe are theclosest of the TE and TM mode fringes to the TIR-PR transition.
 7. Themethod according to claim 1, wherein the capturing of the TE modespectrum and a TM mode spectrum of the glass sample is performed using aprism-coupling system.
 8. The method according to claim 1, wherein thedetermining of the knee stress CSk comprises using the relationshipCSk=[n_(crit) ^(TE)−n_(crit) ^(TM)]/SOC, where n_(crit) ^(TE) andn_(crit) ^(TE) are respective values of the critical-angle effectiveindex at the TIR-PR transitions for the TE and TM mode spectra.
 9. Amethod of measuring knee stress in a chemically strengthenedLi-containing glass sample having a surface and a body and that includesa stress profile having a knee and that defines a waveguide thatsupports light as guided waves and a leaky mode, comprising: capturing aTE mode spectrum and a TM mode spectrum of the guide waves and the leakymode, wherein each mode spectrum has a total internal reflection (TIR)section and a partial-internal reflection (PR) between which resides aTIR-PR transition with a TIR transition location; determining respectiveTIR-PR transition locations for the TE and TM mode spectra; determiningfrom the TE and TM mode spectra a position of the leaky mode relative tothe TIR-PR transitions for the TE and TM mode spectra; determining fromthe leaky mode position an amount of shift in the TIR-PR position foreach of the TM and TE mode spectra as caused by the leaky mode; addingthe amount of shift from the measured position of the TIR-PR transitionto arrive at a corrected TIR-PR transition location for each of the TMand TE mode spectra; and using the corrected TIR-PR transition locationsof the TM and TE mode spectra to determine the knee stress.
 10. Themethod according to claim 9, wherein the TIR-PR transition is defined bya TIR-PR transition intensity profile, the leaky mode has a leaky modeintensity profile, and wherein the determining of the amount of shift inthe TIR-PR position caused by the leaky mode comprises subtracting theleaky mode intensity profile from the TIR-PR transition intensityprofile to define a corrected TIR-PR position of the TIR-PR transition.11. The method according to claim 10, further comprising characterizingthe leaky mode intensity profile by: measuring a breadth of the leakymode intensity profile; measuring a contrast of the leaky mode intensityprofile; and measuring a spacing between the leaky mode and the TIR-PRtransition;
 12. The method according to claim 11, wherein determiningthe position of the leaky mode includes measuring a relative intensityminimum in the partial-internal reflection section and adjacent theTIR-PR transition.
 13. The method according to claim 12, wherein theleaky mode has an intensity profile defined using a digital intensityscale from 0 to 255 using a digital sensor having pixels, and whereinthe intensity minima is 6/255 or less and falls within 30 pixels of theTIR-PR transition.
 14. The method according to claim 12, wherein eachpixel has a size of between 4 microns and 5 microns.
 15. The methodaccording to claim 9, wherein the determining of the knee stress CSkcomprises using the relationship CSk=[n_(crit) ^(TE)−n_(crit)^(TM)]/SOC, where n_(crit) ^(TE) and n_(crit) ^(TE) are respectivevalues of the critical-angle effective index at the TIR-PR transitionsfor the TE and TM mode spectra.
 16. A method of measuring knee stress ina chemically strengthened Li-containing glass sample having a surfaceand a body and that includes a stress profile having a knee and thatdefines a waveguide that supports light as guided modes, comprising:capturing TE mode spectrum and a TM mode spectrum respectivelycomprising TE fringes and TM fringes; measuring a slope SLP of atransition between a total-internal reflection and a partial-internalreflection (TIR-PR) for the light supported by the waveguide for each ofthe TE mode spectrum and the TM mode spectrum; and comparing the slopeto a steepness threshold STH and using the slope to determine a alocation of the TIR-PR transition and using the corrected TIR-PRtransition location to determine the knee stress if the slope is greaterthan the select steepness threshold STH.
 17. The method according toclaim 16, wherein the select steepness threshold STH is defined bymeasuring mode spectra of a reference glass sample for which anacceptable measurement of the knee stress was obtained.
 18. The methodaccording to claim 16, wherein the knee stress measurement has a kneestress measurement error, and wherein the steepness threshold STH isselected such the knee stress measurement error is determined to within+/−15 MPa.
 19. The method according to claim 18, wherein the steepnessthreshold STH is selected such that the knee stress measurement error iswithin +/−10 MPa.
 20. The method according to claim 19, wherein thesteepness threshold STH is selected such that the knee stressmeasurement error within +/−5 MPa.
 21. The method according to claim 16,wherein each TIR-PR transition has an intensity profile whereinmeasuring the slope SLP for each of the TIR-PR transition regions forthe TE mode spectrum and the TM mode spectrum comprises determining alocation of the half-maximum intensity of the TIR-PR transitionintensity profile and measuring the slope SLP at the location of thehalf-maximum intensity of the TIR-PR transition intensity profile. 22.The method according to claim 21, wherein the TIR-PR transition definesa boundary between a TIR section and a PR section of the given TE or TMmode spectrum, and further comprising performing a best fit to theTIR-PR transition intensity profile that omits an overshoot of theintensity on the TIR side of the TIR-PR transition.
 23. The methodaccording to claim 21, wherein the TIR-PR transition intensity profileis measured on a digital intensity scale of 0 to 255 units, and whereinthe steepness threshold STH=−25/255 as measured on the digital intensityscale.
 24. The method according to claim 21, wherein the TIR-PRtransition intensity profile is measured on a digital intensity scale of0 to 255 units, and wherein the steepness threshold STH=−10/255 asmeasured on the digital intensity scale.
 25. The method according toclaim 21, wherein the TIR-PR transition intensity profile is measured ona digital intensity scale of 0 to 255 units, wherein TIR-PR transitiondefines a boundary between a TIR section and a PR section of the givenTE or TM mode spectrum, wherein the TIR-PR transition has an intensityovershoot on the TIR side, and wherein the measurement of the kneestress proceeds only if the intensity overshoot is less than anovershoot tolerance of 30/255 as measured on the digital intensityscale.
 26. The method according to claim 25, wherein the overshoottolerance is 16/255 as measured on the digital intensity scale.
 27. Themethod according to claim 16, further comprising measuring a first widthof at least one TE fringe and a second width of at least one TM fringeand proceeding with determining the knee stress from the TE modespectrum and the TM mode spectrum only if the first and second measuredwidths are within a select width tolerance.
 28. The method according toclaim 27, wherein the width tolerance is defined by measured widths ofTE and TM reference fringes of reference mode spectra of a referenceglass sample for which an acceptable measurement of the knee stress wasobtained.
 29. The method according to claim 27, wherein TE and TMfringes are measured on a digital intensity scale of 0 to 255 unitsusing a sensor having an array of pixels, and proceeding withdetermining the knee stress from the TE mode spectrum and the TM modespectrum only if first and second widths are each smaller than 40pixels.
 30. The method according to claim 29, wherein each pixel has adimension of between 4 microns and 5 microns.
 31. The method accordingto claim 27, wherein TE and TM fringes are measured on a digitalintensity scale of 0 to 255 units using a sensor having an array ofpixels, and proceeding with determining the knee stress from the TE modespectrum and the TM mode spectrum only if first and second widths areeach smaller than 8 pixels.
 32. The method according to claim 31,wherein each pixel has a dimension of between 4 microns and 5 microns.33. The method according to claim 27, wherein: measuring the first widthof at least one TE fringe comprising measuring first widths of multipleTE fringes and defining an average first width; measuring the secondwidth of at least one TM fringe comprising measuring first widths ofmultiple TM fringes and defining an average second width; and comparingthe average first width and the average second width to the select widthtolerance.
 34. The method according to claim 33, wherein TE and TMfringes are measured on a digital intensity scale of 0 to 255 unitsusing a sensor having an array of pixels, and proceeding withdetermining the knee stress from the TE mode spectrum and the TM modespectrum only if first and second average widths are each smaller than40 pixels.
 35. The method according to claim 33, wherein TE and TMfringes are measured on a digital intensity scale of 0 to 255 unitsusing a sensor having an array of pixels, and proceeding withdetermining the knee stress from the TE mode spectrum and the TM modespectrum only if first and second average widths are each smaller than 8pixels.
 36. The method according to claim 35, wherein each pixel has adimension of between 4 microns and 5 microns.
 37. The method accordingto claim 16, wherein the determining of the knee stress CSk comprisesusing the relationship CSk=[n_(crit) ^(TE)−n_(crit) ^(TM)]/SOC, wheren_(crit) ^(TE) and n_(crit) ^(TE) are respective values of thecritical-angle effective index at the TIR-PR transitions for the TE andTM mode spectra.
 38. A method of measuring a knee stress in chemicallystrengthened Li-containing glass samples each having a surface and abody and that includes a stress profile having a knee and that defines awaveguide that supports light as guided modes in the spike region whichhas a monotonically decreasing index profile, comprising: measuring TEand TM mode spectra for each of the multiple glass samples; making adirect measurement of the knee stress using the TE and TM mode spectra;making an indirect measurement of the knee stress that employs thedirect measurements of the knee stress to define a moving-averagedscaling factor for the indirect measurement; and calculating a hybridvalue for the knee stress that using the moving-averaged scaling factorand a birefringence measurement for the sample.
 39. A method ofmeasuring a knee stress in chemically strengthened Li-containing glasssamples each having a surface and a body and that includes a stressprofile having a knee and that defines a waveguide that supports lightas guided modes in the spike region which has a monotonically decreasingindex profile, comprising: measuring TE and TM mode spectra for each ofthe multiple glass samples, wherein the TE and TM mode spectra haverespective TE and TM fringes and respective total-internal reflectionand a partial-internal reflection (TIR-PR) transitions associated with acritical angle and that define respective critical angle effective indexvalues n_(crit) ^(TE) and n_(crit) ^(TM); for each of the measured TEand TM mode spectra, directly measuring a knee stress CSk^(direct) andalso indirectly measuring the knee stress via CSk^(indirect)=β·N₄, whereβ_(x) is a last-mode birefringence and F₄ is a scaling factor;calculating a moving average F₄ ^(average) for the scaling factor F₄using the directly measured knee stresses CSk^(direct) for the multiplesamples via the relationship F₄=CSk^(direct)/β_(x); and calculating ahybrid knee stress CSk^(hybrid)=β_(x)·F₄ ^(average)
 40. The methodaccording to claim 39, wherein directly measuring the knee stressCSk^(direct) is performed using the relationship CSk^(direct)=[n_(crit)^(TE)−n_(crit) ^(TM]/SOC.)
 41. The method according to claim 39, whereinthe moving average includes greater than three values of the scalingfactor F₄.
 42. The method according to claim 39, further comprisingmeasuring a spacing between adjacent TM fringes and starting a newmoving average if the spacing exceeds a fringe spacing tolerance. 43.The method according to claim 39, further comprising determining a depthof layer DOL for each glass sample, calculating a moving average of thedepth of layer DOL, and starting a new moving average of the depth oflayer DOL and for the moving average F₄ ^(average) for the scalingfactor F₄ if a measured depth of layer DOL differs from the movingaverage of the depth of layer DOL by more than 0.7 microns.
 44. A methodof measuring knee stress in a chemically strengthened Li-containingglass sample having a surface and a body and that includes a stressprofile having a knee and that defines a waveguide that supports lightas guided modes, comprising: irradiating the glass sample by directinglight from a light source as a light beam through a coupling prism andto the surface of the sample to generate an angular illuminationspectrum; detecting the angular illumination spectrum at a digitalsensor to capture TE mode spectrum and a TM mode spectrum respectivelycomprising TE fringes and TM fringes and respective total-internalreflection and a partial-internal reflection (TIR-PR) transitionsassociated with a critical angle and that define respective criticalangle effective index values n_(crit) ^(TE) and n_(crit) ^(TM);measuring an intensity gradient in the angular illumination spectrum inthe vicinity of the TIR-PR transitions; and proceeding with themeasurement of the knee stress if the measured intensity gradient isless than an intensity gradient threshold.
 45. The method according toclaim 44 wherein the intensity gradient threshold is determined bymeasuring an intensity gradient from reference glass sample for which anacceptable measurement of the knee stress was obtained.
 46. The methodaccording to claim 44, further comprising correcting the intensitygradient to fall within the intensity gradient threshold by adjustingthe irradiation of the glass sample.
 47. The method according to claim46, wherein said correcting comprises inserting a gradient opticalfilter in the light beam.
 48. The method according to claim 44, whereinthe measuring of the intensity gradient is performed by comparing anintensity distribution of the TE and TM mode spectra as detected by thedigital sensor to a reference intensity.
 49. The method according toclaim 44, wherein the determining of the knee stress CSk comprises usingthe relationship CSk=[n_(crit) ^(TE)−n_(crit) ^(TM)]/SOC.
 50. A methodof performing quality control of an ion-exchange (IOX) process used toform chemically strengthened Li-containing glass samples having asurface and a body and that includes a stress profile having a spike anda knee and that defines a waveguide that supports light as guided modes,comprising: for each of a plurality of glass samples formed by the IOXprocess, measuring TE and TM mode spectra of the guided modes for eachof the glass samples; comparing the measured TE and TM mode spectra toreference TE and TM mode spectra of at least one reference glass sampleformed using the same IOX process and having a flat surface; andadjusting the IOX process to maintain the measured TE and TM modespectra to be within at least one mode spectrum tolerance of thereference TE and TM mode spectra.
 51. The method according to claim 50,wherein the measured TE and TM mode spectrum comprise total-internalreflection and a partial-internal reflection (TIR-PR) transitions havingrespective slopes, wherein the reference TE and TM mode spectrumcomprise TIR-PIR transitions having respective slopes, and wherein atthe least one mode spectrum tolerance comprises the reference slopes,wherein the measured slopes are at least as steep as the referenceslopes.
 52. The method according to claim 50, wherein adjusting the IOXprocess includes first and second in-diffusing ions, and includes atleast one of: adjusting at least one of a first concentration of thefirst in-diffusing ion and a second concentration of the secondin-diffusing ion; adjusting a diffusion temperature; and adjusting asdiffusion time.
 53. The method according to claim 50, wherein the firstand second in-diffusing ions are K+ and Na+ and are exchanged for Li+ions in the glass sample.
 54. The method according to claim 50 whereinthe measured TE and TM mode spectra comprise respective measured TE andTM mode fringes having respective measured widths, the reference TE andTM mode spectra comprise respective reference TE and TM mode fringeshaving respective reference widths, and wherein at the least one modespectrum tolerance comprises the reference widths, wherein the measuredreference widths are the same size or smaller than the reference widths.55. The method according to claim 50, further comprising: determining aknee stress CSk for each glass sample; and comparing the determined kneestress to tolerance range on the knee stress and adjusting the IOXprocess when the determined knee stress falls outside of the tolerancerange.
 56. The method according to claim 55, wherein the knee stresstolerance range is determined from measuring the knee stress of multiplereference glass samples.
 57. The method according to claim 56, whereinthe knee stress tolerance range is 70 Mpa.
 58. The method according toclaim 56, wherein the knee stress tolerance range is 50 Mpa.
 59. Themethod according to claim 55, wherein the determining of the knee stressCSk comprises calculating CSk=[n_(crit) ^(TE)−n_(crit) ^(TM)]/SOC, wheren_(crit) ^(TE) and n_(crit) ^(TE) are respective values of thecritical-angle effective index at the TIR-PR transitions for the TE andTM mode spectra.
 60. The method according to claim 55, wherein the kneestress CSk for each glass sample comprises: directly measuring a kneestress CSk^(direct)=[n_(crit) ^(TE)−n_(crit) ^(TM)]/SOC, where n_(crit)^(TE) and n_(crit) ^(TE) are respective values of the critical-angleeffective index at the TIR-PR transitions for the TE and TM modespectra; indirectly measuring the knee stress viaCSk^(indirect)=β_(x)·F₄, where ⊖_(x) is a last-mode birefringence and F₄is a scaling factor; calculating a moving average F₄ ^(average) for thescaling factor F₄ using the directly measured knee stresses CSk^(direct)for the multiple samples via the relationship F₄=CSk^(direct)/β_(x); andcalculating a hybrid knee stress CSk=CSk^(hybrid)=β_(x)·F₄ ^(average).